Two-dimensional quantum-corrected black hole in a finite size cavity
International Nuclear Information System (INIS)
Zaslavskii, O.B.
2004-01-01
We consider the gravitation-dilaton theory (not necessarily exactly solvable), whose potentials represent a generic linear combination of an exponential and linear functions of the dilaton. A black hole, arising in such theories, is supposed to be enclosed in a cavity, where it attains thermal equilibrium, whereas outside the cavity the field is in the Boulware state. We calculate quantum corrections to the Hawking temperature T H , with the contribution from the boundary taken into account. Vacuum polarization outside the shell tends to cool the system. We find that, for the shell to be in thermal equilibrium, it cannot be placed too close to the horizon. The quantum corrections to the mass due to vacuum polarization vanish in spite of nonzero quantum stresses. We discuss also the canonical boundary conditions and show that accounting for the finiteness of the system plays a crucial role in some theories (e.g., Callan-Giddings-Harvey-Strominger), where it enables us to define the stable canonical ensemble, whereas consideration in an infinite space would predict instability
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Sasaki, Ryu
2011-03-28
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.
Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability
Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.
2018-02-01
As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi
Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.
Pronchik, Jeremy N.; Williams, Brian W.
2003-01-01
Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…
Geometrical aspects of solvable two dimensional models
International Nuclear Information System (INIS)
Tanaka, K.
1989-01-01
It was noted that there is a connection between the non-linear two-dimensional (2D) models and the scalar curvature r, i.e., when r = -2 the equations of motion of the Liouville and sine-Gordon models were obtained. Further, solutions of various classical nonlinear 2D models can be obtained from the condition that the appropriate curvature two form Ω = 0, which suggests that these models are closely related. This relation is explored further in the classical version by obtaining the equations of motion from the evolution equations, the infinite number of conserved quantities, and the common central charge. The Poisson brackets of the solvable 2D models are specified by the Virasoro algebra. 21 refs
Quantum theory of two-dimensional generalized Toda lattice on bounded spatial interval
International Nuclear Information System (INIS)
Leznov, A.N.
1982-01-01
The quantization method of exactly solvable dynamical systems worked out in another paper is applied to a two-dimensional model described by the equations of generalized Toda lattice with a periodicity condition over spatial variable. The Heisenberg operators of the model are finite polynomials over the coupling constant g 2 , whose coefficients functionally depend on operators of noninteracting fields. The model has a direct relation with the string theories and reduces formally when L→infinity to two-dimensional quantum field theory described by the equations of generalized Toda lattice the formal solution of which has been found in Refs
Exactly solvable models of two-dimensional dilaton cosmology with quantum backreaction
International Nuclear Information System (INIS)
Zaslavskii, O B
2003-01-01
We consider a general approach to exactly solvable 2D dilaton cosmology with one-loop backreaction from conformal fields taken into account. It includes as particular cases previous models discussed in the literature. We list different types of solutions and investigate their properties for simple models, typical for string theory. We find a rather rich class of everywhere-regular solutions, which exist practically in every type of analysed solution. They exhibit different kinds of asymptotic behaviour in the past and future, including inflation, superinflation, deflation, power expansion or contraction. In particular, for some models the dS spacetime with a time-dependent dilaton field is the exact solution of the field equations. For some kinds of solution the weak-energy condition is violated independently of a specific model. We also find the solutions with a singularity which is situated in an infinite past (or future), so at any finite moment of a comoving time the universe is singularity-free. It is pointed out that for some models the spacetime may be everywhere regular even in spite of infinitely large quantum backreaction in an infinite past
Solvable potentials derived from supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Levai, G.
1994-01-01
The introduction of supersymmetric quantum mechanics has generated renewed interest in solvable problems of non-relativistic quantum mechanics. This approach offers an elegant way to describe different, but isospectral potentials by interpreting the degeneracy of their energy levels in terms of supersymmetry. The original ideas of supersymmetric quantum mechanics have been developed further in many respects in the past ten years, and have been applied to a large variety of physical problems. The purpose of this contribution is to give a survey of supersymmetric quantum mechanics and its applications to solvable quantum mechanical potentials. Its relation to other models describing isospectral potentials is also discussed here briefly, as well as some of its practical applications in various branches of physics. (orig.)
Gauge dependence and new kind of two-dimensional gravity theory with trivial quantum corrections
International Nuclear Information System (INIS)
Banin, A.T.; Shapiro, I.L.
1993-12-01
We search for the new kinds of classical potentials in two-dimensional induced gravity, which provide the triviality of the one-loop quantum corrections. First of all the gauge dependence of the effective potential is studied. The unique effective potential, introduced by Vilkovisly in 1984 is found to manifest the gauge dependence due to some unusual properties of the theory under consideration. Then we take the gauge of harmonical type, which provides the one-loop finiteness off shell, and then the solution for the required classical potential is found. (author). 35 refs
Some exactly solvable models in quantum mechanics and the low energy expansions
International Nuclear Information System (INIS)
Albeverio, S.; Hoeegh-Krohn, R.; Holden, H.; Gesztesy, F.
We give an overview of recent results on exactly solvable models in quantum mechanics. In particular we discuss point interactions located at finitely or infinitely many centers, in one and three dimensions. Results about the resolvent, energy eigenvalues and resonances, scattering quantitites as well as eigenfunctions and corresponding low energy expansions are mentioned, with particular attention to the case of three-dimensional crystals. (orig.)
An exactly solvable three-dimensional nonlinear quantum oscillator
International Nuclear Information System (INIS)
Schulze-Halberg, A.; Morris, J. R.
2013-01-01
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states
An exactly solvable three-dimensional nonlinear quantum oscillator
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Morris, J. R. [Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2013-11-15
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.
A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
International Nuclear Information System (INIS)
Bravyi, Sergey; Terhal, Barbara
2009-01-01
We study properties of stabilizer codes that permit a local description on a regular D-dimensional lattice. Specifically, we assume that the stabilizer group of a code (the gauge group for subsystem codes) can be generated by local Pauli operators such that the support of any generator is bounded by a hypercube of size O(1). Our first result concerns the optimal scaling of the distance d with the linear size of the lattice L. We prove an upper bound d=O(L D-1 ) which is tight for D=1, 2. This bound applies to both subspace and subsystem stabilizer codes. Secondly, we analyze the suitability of stabilizer codes for building a self-correcting quantum memory. Any stabilizer code with geometrically local generators can be naturally transformed to a local Hamiltonian penalizing states that violate the stabilizer condition. A degenerate ground state of this Hamiltonian corresponds to the logical subspace of the code. We prove that for D=1, 2, different logical states can be mapped into each other by a sequence of single-qubit Pauli errors such that the energy of all intermediate states is upper bounded by a constant independent of the lattice size L. The same result holds if there are unused logical qubits that are treated as 'gauge qubits'. It demonstrates that a self-correcting quantum memory cannot be built using stabilizer codes in dimensions D=1, 2. This result is in sharp contrast with the existence of a classical self-correcting memory in the form of a two-dimensional (2D) ferromagnet. Our results leave open the possibility for a self-correcting quantum memory based on 2D subsystem codes or on 3D subspace or subsystem codes.
Semiclassical analysis of quasiexact solvability
International Nuclear Information System (INIS)
Bender, C.M.; Dunne, G.V.; Moshe, M.
1997-01-01
Higher-order WKB methods are used to investigate the border between the solvable and insolvable portions of the spectrum of quasiexactly solvable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that are central to quasiexact solvability. These two properties define a new class of semiclassically quasiexactly solvable potentials. copyright 1997 The American Physical Society
Classical and quantum contents of solvable game theory on Hilbert space
International Nuclear Information System (INIS)
Cheon, Taksu; Tsutsui, Izumi
2006-01-01
A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be equivalent to a family of classical games supplemented by quantum interference. Our formulation gives a clear perspective to understand why and how quantum strategies outmaneuver classical strategies. It also reveals novel aspects of quantum games such as the stone-scissor-paper phase sub-game and the fluctuation-induced moderation
Quantum mechanics model on a Kaehler conifold
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen
2004-01-01
We propose an exactly solvable model of the quantum oscillator on the class of Kaehler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has nonconstant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction and quantization procedures, the Hamiltonian of the reduced system gets nontrivial quantum corrections. We transform the reduced system into a MIC-Kepler-like one and find that quantum corrections arise only in its energy and coupling constant. We present the exact spectrum of the generalized MIC-Kepler system. The one-(complex) dimensional analog of the suggested model is formulated on the Riemann surface over the complex projective plane and could be interpreted as a system with fractional spin
Directory of Open Access Journals (Sweden)
Orlando Ragnisco
2010-12-01
Full Text Available A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with spherical symmetry. The high number of symmetries (both geometrical and dynamical exhibited by the classical systems has a counterpart in the accidental degeneracy in the spectrum of the quantum systems. This family of quantum problem is completely solved with the techniques of the SUSYQM (supersymmetric quantum mechanics. We also analyze in detail the ordering problem arising in the quantization of the kinetic term of the classical Hamiltonian, stressing the link existing between two physically meaningful quantizations: the geometrical quantization and the position dependent mass quantization.
Fragments of reminiscences and exactly solvable nonrelativistic quantum models
International Nuclear Information System (INIS)
Zakhariev, B.N.
1994-01-01
Some exactly solvable nonrelativistic quantum models are discussed. Special attention is paid to the quantum inverse problem. It is pointed out that by analyzing the inverse problem pictures one can get a deeper insight into the laws of the microworld and acquire the ability to make the qualitative predictions without computers and formulae. 5 refs
Self-correcting quantum computers
International Nuclear Information System (INIS)
Bombin, H; Chhajlany, R W; Horodecki, M; Martin-Delgado, M A
2013-01-01
Is the notion of a quantum computer (QC) resilient to thermal noise unphysical? We address this question from a constructive perspective and show that local quantum Hamiltonian models provide self-correcting QCs. To this end, we first give a sufficient condition on the connectedness of excitations for a stabilizer code model to be a self-correcting quantum memory. We then study the two main examples of topological stabilizer codes in arbitrary dimensions and establish their self-correcting capabilities. Also, we address the transversality properties of topological color codes, showing that six-dimensional color codes provide a self-correcting model that allows the transversal and local implementation of a universal set of operations in seven spatial dimensions. Finally, we give a procedure for initializing such quantum memories at finite temperature. (paper)
Quasi-exact solvability of the one-dimensional Holstein model
International Nuclear Information System (INIS)
Pan Feng; Dai Lianrong; Draayer, J P
2006-01-01
The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is solved by using a Bethe ansatz in analogue to that for the one-dimensional spinless Fermi-Hubbard model. Excitation energies and the corresponding wavefunctions of the model are determined by a set of partial differential equations. It is shown that the model is, at least, quasi-exactly solvable for the two-site case, when the phonon frequency, the electron-phonon coupling strength and the hopping integral satisfy certain relations. As examples, some quasi-exact solutions of the model for the two-site case are derived. (letter to the editor)
A large class of solvable multistate Landau–Zener models and quantum integrability
Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen
2018-06-01
The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians (Sinitsyn et al 2018 Phys. Rev. Lett. 120 190402). Within the multistate Landau–Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models (Sinitsyn and Chernyak 2017 J. Phys. A: Math. Theor. 50 255203). Here we compare both methods by applying them to a new class of exactly solvable MLZ models. This class contains systems with an arbitrary number of interacting states and shows quick growth with N number of exact adiabatic energy crossing points, which appear at different moments of time. At each N, transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with N quickly. We illustrate how common features of solvable MLZ systems appear from quantum integrability and develop an approach to further classification of solvable MLZ problems.
International Nuclear Information System (INIS)
Mankiewicz, L.; Sawicki, M.
1989-01-01
Within a relativistically correct yet analytically solvable model of light-front quantum mechanics we construct the electromagnetic form factor of the two-body bound state and we study the validity of the static approximation to the full form factor. Upon comparison of full form factors calculated for different values of binding energy we observe an unexpected effect that for very strongly bound states further increase in binding leads to an increase in the size of the bound system. A similar effect is found for another quantum-mechanical model of relativistic dynamics
International Nuclear Information System (INIS)
Fradkin, E.S.; Palchik, M.Ya.
1996-02-01
We study a family of exactly solvable models of conformally-invariant quantum field theory in D-dimensional space. We demonstrate the existence of D-dimensional analogs of primary and secondary fields. Under the action of energy-momentum tensor and conserved currents, the primary fields creates an infinite set of (tensor) secondary fields of different generations. The commutators of secondary fields with zero components of current and energy-momentum tensor include anomalous operator terms. We show that the Hilbert space of conformal theory has a special sector which structure is solely defined by the Ward identities independently on the choice of dynamical model. The states of this sector are constructed from secondary fields. Definite self-consistent conditions on the states of the latter sector fix the choice of the field model uniquely. In particular, Lagrangian models do belong to this class of models. The above self-consistent conditions are formulated as follows. Special superpositions Q s , s = 1,2,... of secondary fields are constructed. Each superposition is determined by the requirement that the form of its commutators with energy-momentum tensor and current (i.e. transformation properties) should be identical to that of a primary field. Each equation Q s (x) = 0 is consistent, and defines an exactly solvable model for D ≥ 3. The structure of these models are analogous to that of well-known two dimensional conformal models. The states Q s (x) modul 0> are analogous to the null-vectors of two dimensional theory. In each of these models one can obtain a closed set of differential equations for all the higher Green functions, as well as algebraic equations relating the scale dimension of fundamental field to the D-dimensional analog of a central charge. As an example, we present a detailed discussion of a pair of exactly solvable models in even-dimensional space D ≥ 4. (author). 28 refs
g Algebra and two-dimensional quasiexactly solvable Hamiltonian ...
Indian Academy of Sciences (India)
Keywords. g2 algebra; quasiexactly solvable Hamiltonian; hidden algebra; Poschl–Teller potential. ... space of the polynomials, restricting to a linear transformation on this space, the associ- .... The operators L6 and L7 are the positive root.
A simple method for generating exactly solvable quantum mechanical potentials
Williams, B W
1993-01-01
A simple transformation method permitting the generation of exactly solvable quantum mechanical potentials from special functions solving second-order differential equations is reviewed. This method is applied to Gegenbauer polynomials to generate an attractive radial potential. The relationship of this method to the determination of supersymmetric quantum mechanical superpotentials is discussed, and the superpotential for the radial potential is also derived. (author)
Directory of Open Access Journals (Sweden)
Nicolai Lang, Hans Peter Büchler
2018-01-01
Full Text Available Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the one-dimensional Majorana chain and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.
International Nuclear Information System (INIS)
Kucheryavij, V.Yi.
1994-01-01
The explicit form of nontrivial quantum corrections to Ward identities for AVV- and AAA-current correlators in the four-dimensional world for nondegenerate many-fermion systems of general type is obtained. The characteristics of all nontrivial quantum corrections for nondegenerate two-flavour fermion systems are classified and described. In particular, the well-known results follow from ours for the trivial quantum corrections (anomalies) in the case of the degenerate spectrum of fermion masses
Regularized integrable version of the one-dimensional quantum sine-Gordon model
International Nuclear Information System (INIS)
Japaridze, G.I.; Nersesyan, A.A.; Wiegmann, P.B.
1983-01-01
The authors derive a regularized exactly solvable version of the one-dimensional quantum sine-Gordon model proceeding from the exact solution of the U(1)-symmetric Thirring model. The ground state and the excitation spectrum are obtained in the region ν 2 < 8π. (Auth.)
Experimental two-dimensional quantum walk on a photonic chip.
Tang, Hao; Lin, Xiao-Feng; Feng, Zhen; Chen, Jing-Yuan; Gao, Jun; Sun, Ke; Wang, Chao-Yue; Lai, Peng-Cheng; Xu, Xiao-Yun; Wang, Yao; Qiao, Lu-Feng; Yang, Ai-Lin; Jin, Xian-Min
2018-05-01
Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon-level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems.
Super Virasoro algebra and solvable supersymmetric quantum field theories
International Nuclear Information System (INIS)
Yamanaka, Itaru; Sasaki, Ryu.
1987-09-01
Interesting and deep relationships between super Virasoro algebras and super soliton systems (super KdV, super mKdV and super sine-Gordon equations) are investigated at both classical and quantum levels. An infinite set of conserved quantities responsible for solvability is characterized by super Virasoro algebras only. Several members of the infinite set of conserved quantities are derived explicitly. (author)
Two-dimensional quantum repeaters
Wallnöfer, J.; Zwerger, M.; Muschik, C.; Sangouard, N.; Dür, W.
2016-11-01
The endeavor to develop quantum networks gave rise to a rapidly developing field with far-reaching applications such as secure communication and the realization of distributed computing tasks. This ultimately calls for the creation of flexible multiuser structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multiuser applications. To address this challenge, we propose a two-dimensional quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multiqubit entanglement structures at growing scale, where variants of entanglement swapping and multiparty entanglement purification are combined to create high-fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.
Spin dynamics in a two-dimensional quantum gas
DEFF Research Database (Denmark)
Pedersen, Poul Lindholm; Gajdacz, Miroslav; Deuretzbacher, Frank
2014-01-01
We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimp......We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions...
Three-dimensional quantum algebras: a Cartan-like point of view
International Nuclear Information System (INIS)
Ballesteros, A; Celeghini, E; Olmo, M A del
2004-01-01
A perturbative quantization procedure for Lie bialgebras is introduced. The relevance of the choice of a completely symmetrized basis of the quantum universal enveloping algebra is stressed. Sets of elements of the quantum algebra that play a role similar to generators in the case of Lie algebras are considered and a Cartan-like procedure applied to find a representative for each class of quantum algebras. The method is used to construct and classify all three-dimensional complex quantum algebras that are compatible with a given type of coproduct. The quantization of all Lie algebras that, in the classical limit, belong to the most relevant sector in the classification for three-dimensional Lie bialgebras is thus performed. New quantizations of solvable algebras, whose simplicity makes them suitable for possible physical applications, are obtained and already known related quantum algebras recovered
Quantum logic using correlated one-dimensional quantum walks
Lahini, Yoav; Steinbrecher, Gregory R.; Bookatz, Adam D.; Englund, Dirk
2018-01-01
Quantum Walks are unitary processes describing the evolution of an initially localized wavefunction on a lattice potential. The complexity of the dynamics increases significantly when several indistinguishable quantum walkers propagate on the same lattice simultaneously, as these develop non-trivial spatial correlations that depend on the particle's quantum statistics, mutual interactions, initial positions, and the lattice potential. We show that even in the simplest case of a quantum walk on a one dimensional graph, these correlations can be shaped to yield a complete set of compact quantum logic operations. We provide detailed recipes for implementing quantum logic on one-dimensional quantum walks in two general cases. For non-interacting bosons—such as photons in waveguide lattices—we find high-fidelity probabilistic quantum gates that could be integrated into linear optics quantum computation schemes. For interacting quantum-walkers on a one-dimensional lattice—a situation that has recently been demonstrated using ultra-cold atoms—we find deterministic logic operations that are universal for quantum information processing. The suggested implementation requires minimal resources and a level of control that is within reach using recently demonstrated techniques. Further work is required to address error-correction.
Optical Two-Dimensional Spectroscopy of Disordered Semiconductor Quantum Wells and Quantum Dots
Energy Technology Data Exchange (ETDEWEB)
Cundiff, Steven T. [Univ. of Colorado, Boulder, CO (United States)
2016-05-03
This final report describes the activities undertaken under grant "Optical Two-Dimensional Spectroscopy of Disordered Semiconductor Quantum Wells and Quantum Dots". The goal of this program was to implement optical 2-dimensional Fourier transform spectroscopy and apply it to electronic excitations, including excitons, in semiconductors. Specifically of interest are quantum wells that exhibit disorder due to well width fluctuations and quantum dots. In both cases, 2-D spectroscopy will provide information regarding coupling among excitonic localization sites.
Engineering two-photon high-dimensional states through quantum interference
Zhang, Yingwen; Roux, Filippus S.; Konrad, Thomas; Agnew, Megan; Leach, Jonathan; Forbes, Andrew
2016-01-01
Many protocols in quantum science, for example, linear optical quantum computing, require access to large-scale entangled quantum states. Such systems can be realized through many-particle qubits, but this approach often suffers from scalability problems. An alternative strategy is to consider a lesser number of particles that exist in high-dimensional states. The spatial modes of light are one such candidate that provides access to high-dimensional quantum states, and thus they increase the storage and processing potential of quantum information systems. We demonstrate the controlled engineering of two-photon high-dimensional states entangled in their orbital angular momentum through Hong-Ou-Mandel interference. We prepare a large range of high-dimensional entangled states and implement precise quantum state filtering. We characterize the full quantum state before and after the filter, and are thus able to determine that only the antisymmetric component of the initial state remains. This work paves the way for high-dimensional processing and communication of multiphoton quantum states, for example, in teleportation beyond qubits. PMID:26933685
Quantum Communication Through a Two-Dimensional Spin Network
International Nuclear Information System (INIS)
Wang Zhaoming; Gu Yongjian
2012-01-01
We investigate the state or entanglement transfer through a two-dimensional spin network. We show that for state transfer, better fidelity can be gained along the diagonal direction but for entanglement transfer, when the initial entanglement is created along the boundary, the concurrence is more inclined to propagate along the boundary. This behavior is produced by quantum mechanical interference and the communication quality depends on the precise size of the network. For some number of sites, the fidelity in a two-dimensional channel is higher than one-dimensional case. This is an important result for realizing quantum communication through high dimension spin chain networks.
Construction of two-dimensional quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Klimek, S.; Kondracki, W.
1987-12-01
We present a sketch of the construction of the functional measure for the SU(2) quantum chromodynamics with one generation of fermions in two-dimensional space-time. The method is based on a detailed analysis of Wilson loops.
Quantum oscillations in quasi-two-dimensional conductors
Galbova, O
2002-01-01
The electronic absorption of sound waves in quasi-two-dimensional conductors in strong magnetic fields, is investigated theoretically. A longitudinal acoustic wave, propagating along the normal n-> to the layer of quasi-two-dimensional conductor (k-> = left brace 0,0,k right brace; u-> = left brace 0,0,u right brace) in magnetic field (B-> = left brace 0, 0, B right brace), is considered. The quasiclassical approach for this geometry is of no interest, due to the absence of interaction between electromagnetic and acoustic waves. The problem is of interest in strong magnetic field when quantization of the charge carriers energy levels takes place. The quantum oscillations in the sound absorption coefficient, as a function of the magnetic field, are theoretically observed. The experimental study of the quantum oscillations in quasi-two-dimensional conductors makes it possible to solve the inverse problem of determining from experimental data the extrema closed sections of the Fermi surface by a plane p sub z = ...
Prepotential approach to exact and quasi-exact solvabilities
International Nuclear Information System (INIS)
Ho, C.-L.
2008-01-01
Exact and quasi-exact solvabilities of the one-dimensional Schroedinger equation are discussed from a unified viewpoint based on the prepotential together with Bethe ansatz equations. This is a constructive approach which gives the potential as well as the eigenfunctions and eigenvalues simultaneously. The novel feature of the present work is the realization that both exact and quasi-exact solvabilities can be solely classified by two integers, the degrees of two polynomials which determine the change of variable and the zeroth order prepotential. Most of the well-known exactly and quasi-exactly solvable models, and many new quasi-exactly solvable ones, can be generated by appropriately choosing the two polynomials. This approach can be easily extended to the constructions of exactly and quasi-exactly solvable Dirac, Pauli, and Fokker-Planck equations
International Nuclear Information System (INIS)
Ushveridze, A.G.
1992-01-01
This paper reports that quasi-exactly solvable (QES) models realize principally new type of exact solvability in quantum physics. These models are distinguished by the fact that the Schrodinger equations for them can be solved exactly only for certain limited parts of the spectrum, but not for the whole spectrum. They occupy an intermediate position between the exactly the authors solvable (ES) models and all the others. The number of energy levels for which the spectral problems can be solved exactly refer below to as the order of QES model. From the mathematical point of view the existence of QES models is not surprising. Indeed, if the term exact solvability expresses the possibility of total explicit diagonalization of infinite Hamiltonian matrix, then the term quasi-exact solvability implies the situation when the Hamiltonian matrix can be reduced explicitly to the block-diagonal form with one of the appearing blocks being finite
Two-point entanglement near a quantum phase transition
International Nuclear Information System (INIS)
Chen, Han-Dong
2007-01-01
In this work, we study the two-point entanglement S(i, j), which measures the entanglement between two separated degrees of freedom (ij) and the rest of system, near a quantum phase transition. Away from the critical point, S(i, j) saturates with a characteristic length scale ξ E , as the distance |i - j| increases. The entanglement length ξ E agrees with the correlation length. The universality and finite size scaling of entanglement are demonstrated in a class of exactly solvable one-dimensional spin model. By connecting the two-point entanglement to correlation functions in the long range limit, we argue that the prediction power of a two-point entanglement is universal as long as the two involved points are separated far enough
Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model
Pont, Federico M.; Osenda, Omar; Serra, Pablo
2018-05-01
The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.
Operator quantum error-correcting subsystems for self-correcting quantum memories
International Nuclear Information System (INIS)
Bacon, Dave
2006-01-01
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general notion of quantum error correction known as operator quantum error correction. In standard quantum error-correcting codes, one requires the ability to apply a procedure which exactly reverses on the error-correcting subspace any correctable error. In contrast, for operator error-correcting subsystems, the correction procedure need not undo the error which has occurred, but instead one must perform corrections only modulo the subsystem structure. This does not lead to codes which differ from subspace codes, but does lead to recovery routines which explicitly make use of the subsystem structure. Here we present two examples of such operator error-correcting subsystems. These examples are motivated by simple spatially local Hamiltonians on square and cubic lattices. In three dimensions we provide evidence, in the form a simple mean field theory, that our Hamiltonian gives rise to a system which is self-correcting. Such a system will be a natural high-temperature quantum memory, robust to noise without external intervening quantum error-correction procedures
Entropic Barriers for Two-Dimensional Quantum Memories
Brown, Benjamin J.; Al-Shimary, Abbas; Pachos, Jiannis K.
2014-03-01
Comprehensive no-go theorems show that information encoded over local two-dimensional topologically ordered systems cannot support macroscopic energy barriers, and hence will not maintain stable quantum information at finite temperatures for macroscopic time scales. However, it is still well motivated to study low-dimensional quantum memories due to their experimental amenability. Here we introduce a grid of defect lines to Kitaev's quantum double model where different anyonic excitations carry different masses. This setting produces a complex energy landscape which entropically suppresses the diffusion of excitations that cause logical errors. We show numerically that entropically suppressed errors give rise to superexponential inverse temperature scaling and polynomial system size scaling for small system sizes over a low-temperature regime. Curiously, these entropic effects are not present below a certain low temperature. We show that we can vary the system to modify this bound and potentially extend the described effects to zero temperature.
Decoherence in two-dimensional quantum walks
International Nuclear Information System (INIS)
Oliveira, A. C.; Portugal, R.; Donangelo, R.
2006-01-01
We analyze the decoherence in quantum walks in two-dimensional lattices generated by broken-link-type noise. In this type of decoherence, the links of the lattice are randomly broken with some given constant probability. We obtain the evolution equation for a quantum walker moving on two-dimensional (2D) lattices subject to this noise, and we point out how to generalize for lattices in more dimensions. In the nonsymmetric case, when the probability of breaking links in one direction is different from the probability in the perpendicular direction, we have obtained a nontrivial result. If one fixes the link-breaking probability in one direction, and gradually increases the probability in the other direction from 0 to 1, the decoherence initially increases until it reaches a maximum value, and then it decreases. This means that, in some cases, one can increase the noise level and still obtain more coherence. Physically, this can be explained as a transition from a decoherent 2D walk to a coherent 1D walk
Solvable quantum two-body problem: entanglement
International Nuclear Information System (INIS)
Glasser, M L; Nieto, L M
2005-01-01
A simple one-dimensional model is introduced describing a two particle 'atom' approaching a point at which the interaction between the particles is lost. The wavefunction is obtained analytically and analysed to display the entangled nature of the subsequent state. (letter to the editor)
Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
Energy Technology Data Exchange (ETDEWEB)
Pastawski, Fernando; Yoshida, Beni [Institute for Quantum Information & Matter and Walter Burke Institute for Theoretical Physics,California Institute of Technology,1200 E. California Blvd., Pasadena CA 91125 (United States); Harlow, Daniel [Princeton Center for Theoretical Science, Princeton University,400 Jadwin Hall, Princeton NJ 08540 (United States); Preskill, John [Institute for Quantum Information & Matter and Walter Burke Institute for Theoretical Physics,California Institute of Technology,1200 E. California Blvd., Pasadena CA 91125 (United States)
2015-06-23
We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an isometry from the bulk Hilbert space to the boundary Hilbert space. The entire tensor network is an encoder for a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. That bulk logical operators can be represented on multiple boundary regions mimics the Rindler-wedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed in http://dx.doi.org/10.1007/JHEP04(2015)163.
Hall Conductivity in a Quasi-Two-Dimensional Disordered Electron System
Institute of Scientific and Technical Information of China (English)
YANG Yong-Hong; WANG Yong-Gang; LIU Mei
2002-01-01
By making use of the diagrammatic techniques in perturbation theory,we have investigated the Hall effect in a quasi-two-dimensional disordered electron system.In the weakly localized regime,the analytical expression for quantum correction to Hall conductivity has been obtained using the Kubo formalism and quasiclassical approximation.The relevant dimensional crossover behavior from three dimensions to two dimensions with decreasing the interlayer hopping energy is discussed.The quantum interference effect is shown to have a vanishing correction t,o the Hall coefficient.
Two-dimensional electron gas in monolayer InN quantum wells
International Nuclear Information System (INIS)
Pan, W.; Wang, G. T.; Dimakis, E.; Moustakas, T. D.; Tsui, D. C.
2014-01-01
We report in this letter experimental results that confirm the two-dimensional nature of the electron systems in a superlattice structure of 40 InN quantum wells consisting of one monolayer of InN embedded between 10 nm GaN barriers. The electron density and mobility of the two-dimensional electron system (2DES) in these InN quantum wells are 5 × 10 15 cm −2 (or 1.25 × 10 14 cm −2 per InN quantum well, assuming all the quantum wells are connected by diffused indium contacts) and 420 cm 2 /Vs, respectively. Moreover, the diagonal resistance of the 2DES shows virtually no temperature dependence in a wide temperature range, indicating the topological nature of the 2DES
Unruly topologies in two-dimensional quantum gravity
International Nuclear Information System (INIS)
Hartle, J.B.
1985-01-01
A sum over histories formulation of quantum geometry could involve sums over different topologies as well as sums over different metrics. In classical gravity a geometry is a manifold with a metric, but it is difficult to implement a sum over manifolds in quantum gravity. In this difficulty, motivation is found for including in the sum over histories, geometries defined on more general objects than manifolds-unruly topologies. In simplicial two-dimensional quantum gravity a class of simplicial complexes is found to which the gravitational action can be extended, for which sums over the class are straightforwardly defined, and for which a manifold dominates the sum in the classical limit. The situation in higher dimensions is discussed. (author)
Quantum wave packet revival in two-dimensional circular quantum wells with position-dependent mass
International Nuclear Information System (INIS)
Schmidt, Alexandre G.M.; Azeredo, Abel D.; Gusso, A.
2008-01-01
We study quantum wave packet revivals on two-dimensional infinite circular quantum wells (CQWs) and circular quantum dots with position-dependent mass (PDM) envisaging a possible experimental realization. We consider CQWs with radially varying mass, addressing particularly the cases where M(r)∝r w with w=1,2, or -2. The two PDM Hamiltonians currently allowed by theory were analyzed and we were able to construct a strong theoretical argument favoring one of them
Self-correcting quantum memory in a thermal environment
International Nuclear Information System (INIS)
Chesi, Stefano; Roethlisberger, Beat; Loss, Daniel
2010-01-01
The ability to store information is of fundamental importance to any computer, be it classical or quantum. To identify systems for quantum memories, which rely, analogously to classical memories, on passive error protection (''self-correction''), is of greatest interest in quantum information science. While systems with topological ground states have been considered to be promising candidates, a large class of them was recently proven unstable against thermal fluctuations. Here, we propose two-dimensional (2D) spin models unaffected by this result. Specifically, we introduce repulsive long-range interactions in the toric code and establish a memory lifetime polynomially increasing with the system size. This remarkable stability is shown to originate directly from the repulsive long-range nature of the interactions. We study the time dynamics of the quantum memory in terms of diffusing anyons and support our analytical results with extensive numerical simulations. Our findings demonstrate that self-correcting quantum memories can exist in 2D at finite temperatures.
Quantum wave packet revival in two-dimensional circular quantum wells with position-dependent mass
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Alexandre G.M. [Departamento de Ciencias Exatas, Polo Universitario de Volta Redonda-Universidade Federal Fluminense, Av. dos Trabalhadores 420, Volta Redonda RJ, CEP 27255-125 (Brazil)], E-mail: agmschmidt@gmail.com; Azeredo, Abel D. [Departamento de Fisica-Universidade Federal de Roraima, Av. Cap. Ene Garcez 2413, Boa Vista RR, CEP 69304-000 (Brazil)], E-mail: aazeredo@gmail.com; Gusso, A. [Departamento de Ciencias Exatas e Tecnologicas-Universidade Estadual de Santa Cruz, km 16 Rodovia Ilheus-Itabuna, Ilheus BA, CEP 45662-000 (Brazil)], E-mail: agusso@uesc.br
2008-04-14
We study quantum wave packet revivals on two-dimensional infinite circular quantum wells (CQWs) and circular quantum dots with position-dependent mass (PDM) envisaging a possible experimental realization. We consider CQWs with radially varying mass, addressing particularly the cases where M(r){proportional_to}r{sup w} with w=1,2, or -2. The two PDM Hamiltonians currently allowed by theory were analyzed and we were able to construct a strong theoretical argument favoring one of them.
An introduction to integrable techniques in one-dimensional quantum systems
Franchini, Fabio
2017-01-01
This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and t...
Two-dimensional color-code quantum computation
International Nuclear Information System (INIS)
Fowler, Austin G.
2011-01-01
We describe in detail how to perform universal fault-tolerant quantum computation on a two-dimensional color code, making use of only nearest neighbor interactions. Three defects (holes) in the code are used to represent logical qubits. Triple-defect logical qubits are deformed into isolated triangular sections of color code to enable transversal implementation of all single logical qubit Clifford group gates. Controlled-NOT (CNOT) is implemented between pairs of triple-defect logical qubits via braiding.
International Nuclear Information System (INIS)
Duque, C.M.; Morales, A.L.; Mora-Ramos, M.E.; Duque, C.A.
2013-01-01
The linear and nonlinear optical absorption as well as the linear and nonlinear corrections to the refractive index are calculated in a disc shaped quantum dot under the effect of an external magnetic field and parabolic and inverse square confining potentials. The exact solutions for the two-dimensional motion of the conduction band electrons are used as the basis for a perturbation-theory treatment of the effect of a static applied electric field. In general terms, the variation of one of the different potential energy parameters – for a fixed configuration of the remaining ones – leads to either blueshifts or redshifts of the resonant peaks as well as to distinct rates of change for their amplitudes. -- Highlights: • Optical absorption and corrections to the refractive in quantum dots. • Electric and magnetic field and parabolic and inverse square potentials. • Perturbation-theory treatment of the effect of the electric field. • Induced blueshifts or redshifts of the resonant peaks are studied. • Evolution of rates of change for amplitudes of resonant peaks
Energy Technology Data Exchange (ETDEWEB)
Duque, C.M., E-mail: cduque@fisica.udea.edu.co [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia); Morales, A.L. [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia); Mora-Ramos, M.E. [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia); Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, CP 62209, Cuernavaca, Morelos (Mexico); Duque, C.A. [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia)
2013-11-15
The linear and nonlinear optical absorption as well as the linear and nonlinear corrections to the refractive index are calculated in a disc shaped quantum dot under the effect of an external magnetic field and parabolic and inverse square confining potentials. The exact solutions for the two-dimensional motion of the conduction band electrons are used as the basis for a perturbation-theory treatment of the effect of a static applied electric field. In general terms, the variation of one of the different potential energy parameters – for a fixed configuration of the remaining ones – leads to either blueshifts or redshifts of the resonant peaks as well as to distinct rates of change for their amplitudes. -- Highlights: • Optical absorption and corrections to the refractive in quantum dots. • Electric and magnetic field and parabolic and inverse square potentials. • Perturbation-theory treatment of the effect of the electric field. • Induced blueshifts or redshifts of the resonant peaks are studied. • Evolution of rates of change for amplitudes of resonant peaks.
C*-algebraic scattering theory and explicitly solvable quantum field theories
International Nuclear Information System (INIS)
Warchall, H.A.
1985-01-01
A general theoretical framework is developed for the treatment of a class of quantum field theories that are explicitly exactly solvable, but require the use of C*-algebraic techniques because time-dependent scattering theory cannot be constructed in any one natural representation of the observable algebra. The purpose is to exhibit mechanisms by which inequivalent representations of the observable algebra can arise in quantum field theory, in a setting free of other complications commonly associated with the specification of dynamics. One of two major results is the development of necessary and sufficient conditions for the concurrent unitary implementation of two automorphism groups in a class of quasifree representations of the algebra of the canonical commutation relations (CCR). The automorphism groups considered are induced by one-parameter groups of symplectic transformations on the classical phase space over which the Weyl algebra of the CCR is built; each symplectic group is conjugate by a fixed symplectic transformation to a one-parameter unitary group. The second result, an analog to the Birman--Belopol'skii theorem in two-Hilbert-space scattering theory, gives sufficient conditions for the existence of Moller wave morphisms in theories with time-development automorphism groups of the above type. In a paper which follows, this framework is used to analyze a particular model system for which wave operators fail to exist in any natural representation of the observable algebra, but for which wave morphisms and an associated S matrix are easily constructed
Exactly solvable birth and death processes
International Nuclear Information System (INIS)
Sasaki, Ryu
2009-01-01
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q x (with x being the population) corresponding to the q-Racah polynomial.
Efficient construction of two-dimensional cluster states with probabilistic quantum gates
International Nuclear Information System (INIS)
Chen Qing; Cheng Jianhua; Wang Kelin; Du Jiangfeng
2006-01-01
We propose an efficient scheme for constructing arbitrary two-dimensional (2D) cluster states using probabilistic entangling quantum gates. In our scheme, the 2D cluster state is constructed with starlike basic units generated from 1D cluster chains. By applying parallel operations, the process of generating 2D (or higher-dimensional) cluster states is significantly accelerated, which provides an efficient way to implement realistic one-way quantum computers
International Nuclear Information System (INIS)
Gelman, David; Schwartz, Steven D.
2010-01-01
The recently developed quantum-classical method has been applied to the study of dissipative dynamics in multidimensional systems. The method is designed to treat many-body systems consisting of a low dimensional quantum part coupled to a classical bath. Assuming the approximate zeroth order evolution rule, the corrections to the quantum propagator are defined in terms of the total Hamiltonian and the zeroth order propagator. Then the corrections are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The evolution of the primary part is governed by the corrected propagator yielding the exact quantum dynamics. The method has been tested on two model systems coupled to a harmonic bath: (i) an anharmonic (Morse) oscillator and (ii) a double-well potential. The simulations have been performed at zero temperature. The results have been compared to the exact quantum simulations using the surrogate Hamiltonian approach.
False vacuum decay in quantum mechanics and four dimensional scalar field theory
Bezuglov, Maxim
2018-04-01
When the Higgs boson was discovered in 2012 it was realized that electroweak vacuum may suffer a possible metastability on the Planck scale and can eventually decay. To understand this problem it is important to have reliable predictions for the vacuum decay rate within the framework of quantum field theory. For now, it can only be done at one loop level, which is apparently is not enough. The aim of this work is to develop a technique for the calculation of two and higher order radiative corrections to the false vacuum decay rate in the framework of four dimensional scalar quantum field theory and then apply it to the case of the Standard Model. To achieve this goal, we first start from the case of d=1 dimensional QFT i.e. quantum mechanics. We show that for some potentials two and three loop corrections can be very important and must be taken into account. Next, we use quantum mechanical example as a template for the general d=4 dimensional theory. In it we are concentrating on the calculations of bounce solution and corresponding Green function in so called thin wall approximation. The obtained Green function is then used as a main ingredient for the calculation of two loop radiative corrections to the false vacuum decay rate.
Koren, B.; Hackbusch, W.; Trottenberg, U.
1991-01-01
Two simple, multi-dimensional upwind discretizations for the steady Euler equations are derived, with the emphasis Iying on bath a good accuracy and a good solvability. The multi-dimensional upwinding consists of applying a one-dimensional Riemann solver with a locally rotated left and right state,
Two-dimensional quantum electrodynamics as a model in the constructive quantum field theory
International Nuclear Information System (INIS)
Ito, K.R.
1976-01-01
We investigate two-dimensional quantum electrodynamics((QED) 2 ) type models on the basis of the Hamiltonian formalism of a vector field. The transformation into a sine-Gordon equation is clarified as a generalized mass-shift transformation through canonical linear transformations. (auth.)
Exactly solvable models in many-body theory
March, N H
2016-01-01
The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.
Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection
Chamon, Claudio
2005-01-01
This Letter presents solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three-dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, (1)have no quenched disorder, (2)have solely local interactions, (3)have an exactly solvable spectrum, (4)have topologically ordered ground states, and (5)have slow dynamical relaxation rates akin to those of strong structural glasses.
Two dimensional electron systems for solid state quantum computation
Mondal, Sumit
Two dimensional electron systems based on GaAs/AlGaAs heterostructures are extremely useful in various scientific investigations of recent times including the search for quantum computational schemes. Although significant strides have been made over the past few years to realize solid state qubits on GaAs/AlGaAs 2DEGs, there are numerous factors limiting the progress. We attempt to identify factors that have material and design-specific origin and develop ways to overcome them. The thesis is divided in two broad segments. In the first segment we describe the realization of a new field-effect induced two dimensional electron system on GaAs/AlGaAs heterostructure where the novel device-design is expected to suppress the level of charge noise present in the device. Modulation-doped GaAs/AlGaAs heterostructures are utilized extensively in the study of quantum transport in nanostructures, but charge fluctuations associated with remote ionized dopants often produce deleterious effects. Electric field-induced carrier systems offer an attractive alternative if certain challenges can be overcome. We demonstrate a field-effect transistor in which the active channel is locally devoid of modulation-doping, but silicon dopant atoms are retained in the ohmic contact region to facilitate low-resistance contacts. A high quality two-dimensional electron gas is induced by a field-effect that is tunable over a density range of 6.5x10 10cm-2 to 2.6x1011cm-2 . Device design, fabrication, and low temperature (T=0.3K) characterization results are discussed. The demonstrated device-design overcomes several existing limitations in the fabrication of field-induced 2DEGs and might find utility in hosting nanostructures required for making spin qubits. The second broad segment describes our effort to correlate transport parameters measured at T=0.3K to the strength of the fractional quantum Hall state observed at nu=5/2 in the second Landau level of high-mobility GaAs/AlGaAs two dimensional
Topics in Covariant Closed String Field Theory and Two-Dimensional Quantum Gravity
Saadi, Maha
1991-01-01
The closed string field theory based on the Witten vertex is found to be nonpolynomial in order to reproduce all tree amplitudes correctly. The interactions have a geometrical pattern of overlaps, which can be thought as the edges of a spherical polyhedron with face-perimeters equal to 2pi. At each vertex of the polyhedron there are three faces, thus all elementary interactions are cubic in the sense that at most three strings can coincide at a point. The quantum action is constructed by substracting counterterms which cancel the overcounting of moduli space, and by adding loop vertices in such a way no possible surfaces are missed. A counterterm that gives the correct one-string one-loop amplitude is formulated. The lowest order loop vertices are analyzed in the cases of genus one and two. Also, a one-loop two -string counterterm that restores BRST invariance to the respective scattering amplitude is constructed. An attempt to understand the formulation of two -dimensional pure gravity from the discrete representation of a two-dimensional surface is made. This is considered as a toy model of string theory. A well-defined mathematical model is used. Its continuum limit cannot be naively interpreted as pure gravity because each term of the sum over surfaces is not positive definite. The model, however, could be considered as an analytic continuation of the standard matrix model formulation of gravity. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).
The quantum spectral analysis of the two-dimensional annular billiard system
International Nuclear Information System (INIS)
Yan-Hui, Zhang; Ji-Quan, Zhang; Xue-You, Xu; Sheng-Lu, Lin
2009-01-01
Based on the extended closed-orbit theory together with spectral analysis, this paper studies the correspondence between quantum mechanics and the classical counterpart in a two-dimensional annular billiard. The results demonstrate that the Fourier-transformed quantum spectra are in very good accordance with the lengths of the classical ballistic trajectories, whereas spectral strength is intimately associated with the shapes of possible open orbits connecting arbitrary two points in the annular cavity. This approach facilitates an intuitive understanding of basic quantum features such as quantum interference, locations of the wavefunctions, and allows quantitative calculations in the range of high energies, where full quantum calculations may become impractical in general. This treatment provides a thread to explore the properties of microjunction transport and even quantum chaos under the much more general system. (general)
International Nuclear Information System (INIS)
Nevedomskiy, V. N.; Bert, N. A.; Chaldyshev, V. V.; Preobrazhernskiy, V. V.; Putyato, M. A.; Semyagin, B. R.
2015-01-01
A single molecular-beam epitaxy process is used to produce GaAs-based heterostructures containing two-dimensional arrays of InAs semiconductor quantum dots and AsSb metal quantum dots. The twodimensional array of AsSb metal quantum dots is formed by low-temperature epitaxy which provides a large excess of arsenic in the epitaxial GaAs layer. During the growth of subsequent layers at a higher temperature, excess arsenic forms nanoinclusions, i.e., metal quantum dots in the GaAs matrix. The two-dimensional array of such metal quantum dots is created by the δ doping of a low-temperature GaAs layer with antimony which serves as a precursor for the heterogeneous nucleation of metal quantum dots and accumulates in them with the formation of AsSb metal alloy. The two-dimensional array of InAs semiconductor quantum dots is formed via the Stranski–Krastanov mechanism at the GaAs surface. Between the arrays of metal and semiconductor quantum dots, a 3-nm-thick AlAs barrier layer is grown. The total spacing between the arrays of metal and semiconductor quantum dots is 10 nm. Electron microscopy of the structure shows that the arrangement of metal quantum dots and semiconductor quantum dots in the two-dimensional arrays is spatially correlated. The spatial correlation is apparently caused by elastic strain and stress fields produced by both AsSb metal and InAs semiconductor quantum dots in the GaAs matrix
Energy Spectra of Vortex Distributions in Two-Dimensional Quantum Turbulence
Directory of Open Access Journals (Sweden)
Ashton S. Bradley
2012-10-01
Full Text Available We theoretically explore key concepts of two-dimensional turbulence in a homogeneous compressible superfluid described by a dissipative two-dimensional Gross-Pitaeveskii equation. Such a fluid supports quantized vortices that have a size characterized by the healing length ξ. We show that, for the divergence-free portion of the superfluid velocity field, the kinetic-energy spectrum over wave number k may be decomposed into an ultraviolet regime (k≫ξ^{-1} having a universal k^{-3} scaling arising from the vortex core structure, and an infrared regime (k≪ξ^{-1} with a spectrum that arises purely from the configuration of the vortices. The Novikov power-law distribution of intervortex distances with exponent -1/3 for vortices of the same sign of circulation leads to an infrared kinetic-energy spectrum with a Kolmogorov k^{-5/3} power law, which is consistent with the existence of an inertial range. The presence of these k^{-3} and k^{-5/3} power laws, together with the constraint of continuity at the smallest configurational scale k≈ξ^{-1}, allows us to derive a new analytical expression for the Kolmogorov constant that we test against a numerical simulation of a forced homogeneous, compressible, two-dimensional superfluid. The numerical simulation corroborates our analysis of the spectral features of the kinetic-energy distribution, once we introduce the concept of a clustered fraction consisting of the fraction of vortices that have the same sign of circulation as their nearest neighboring vortices. Our analysis presents a new approach to understanding two-dimensional quantum turbulence and interpreting similarities and differences with classical two-dimensional turbulence, and suggests new methods to characterize vortex turbulence in two-dimensional quantum fluids via vortex position and circulation measurements.
International Nuclear Information System (INIS)
Pal, Karoly F.; Vertesi, Tamas
2010-01-01
The I 3322 inequality is the simplest bipartite two-outcome Bell inequality beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In the case of the CHSH inequality the maximal quantum violation can already be attained with local two-dimensional quantum systems; however, there is no such evidence for the I 3322 inequality. In this paper a family of measurement operators and states is given which enables us to attain the maximum quantum value in an infinite-dimensional Hilbert space. Further, it is conjectured that our construction is optimal in the sense that measuring finite-dimensional quantum systems is not enough to achieve the true quantum maximum. We also describe an efficient iterative algorithm for computing quantum maximum of an arbitrary two-outcome Bell inequality in any given Hilbert space dimension. This algorithm played a key role in obtaining our results for the I 3322 inequality, and we also applied it to improve on our previous results concerning the maximum quantum violation of several bipartite two-outcome Bell inequalities with up to five settings per party.
Higher dimensional loop quantum cosmology
International Nuclear Information System (INIS)
Zhang, Xiangdong
2016-01-01
Loop quantum cosmology (LQC) is the symmetric sector of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogeneous cosmological model in n + 1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n + 1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n + 1 dimensional model and the 3 + 1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers the possibility to investigate quantum gravity effects in higher dimensional cosmology. (orig.)
Chemically Triggered Formation of Two-Dimensional Epitaxial Quantum Dot Superlattices
Walravens, Willem; De Roo, Jonathan; Drijvers, Emile; Ten Brinck, Stephanie; Solano, Eduardo; Dendooven, Jolien; Detavernier, Christophe; Infante, Ivan; Hens, Zeger
2016-01-01
Two dimensional superlattices of epitaxially connected quantum dots enable size-quantization effects to be combined with high charge carrier mobilities, an essential prerequisite for highly performing QD devices based on charge transport. Here, we demonstrate that surface active additives known to
International Nuclear Information System (INIS)
Tseytlin, A.A.
1993-01-01
We consider a two-dimensional sigma model with a (2+N)-dimensional Minkowski signature target space metric having a covariantly constant null Killing vector. We study solutions of the conformal invariance conditions in 2+N dimensions and find that generic solutions can be represented in terms of the RG flow in N-dimensional 'transverse space' theory. The resulting conformal invariant sigma model is interpreted as a quantum action of the two-dimensional scalar ('dilaton') quantum gravity model coupled to a (non-conformal) 'transverse' sigma model. The conformal factor of the two-dimensional metric is identified with a light-cone coordinate of the (2+N)-dimensional sigma model. We also discuss the case when the transverse theory is conformal (with or without the antisymmetric tensor background) and reproduce in a systematic way the solutions with flat transverse space known before. (orig.)
On the exact spectra of two electrons confined by two-dimensional quantum dots
International Nuclear Information System (INIS)
Soldatov, A.V.; Bogolubov Jr, N.N.
2005-12-01
Applicability of the method of intermediate problems to investigation of the energy spectrum and eigenstates of a two- electron two-dimensional quantum dot (QD) formed by a parabolic confining potential is discussed. It is argued that the method of intermediate problems, which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian operators in Hilbert space, can be fused with the classical Rayleigh-Ritz variational method and stochastic variational method thus providing an efficient tool of verification of the results obtained so far by various analytical and numerical methods being of current usage for studies of quantum dot models. (author)
International Nuclear Information System (INIS)
Bakke, K.; Furtado, C.
2012-01-01
We study the quantum dynamics of a neutral particle in the Aharonov-Casher system and in the Landau-Aharonov-Casher system confined to a two-dimensional quantum ring, a quantum dot, and a quantum anti-dot potentials described by the Tan-Inkson model [W.-C. Tan and J. C. Inkson, Semicond. Sci. Technol. 11, 1635 (1996)]. We show, in the Aharonov-Casher system, that bound states can be achieved when the neutral particle is confined to the two-dimensional quantum ring and the quantum dot and discuss the appearance of persistent currents. In the Landau-Aharonov-Casher system, we show that bound states can be achieved when the neutral particle is confined to the quantum anti-dot, quantum dot, and the two-dimensional quantum ring, but there are no persistent currents.
Dilaton quantum cosmology in two dimensions
International Nuclear Information System (INIS)
Mazzitelli, F.D.; Russo, J.G.
1992-11-01
We consider a renormalizable two-dimensional model of dilaton gravity coupled to a set of conformal fields as a toy model for quantum cosmology. We discuss the cosmological solutions of the model and study the effect of including the back reaction due to quantum corrections. As a result, when the matter density is below some threshold new singularities form in a weak coupling region, which suggests that they will not be removed in full quantum theory. We also solve the Wheeler-DeWitt equation. Depending on the quantum state of the Universe, the singularities may appear in a quantum region where the wave function is not oscillatory, i.e., when there is not a well defined notion of classical spacetime. (author). 29 refs, 4 figs
International Nuclear Information System (INIS)
Horing, N.J.M.; Yildiz, M.M.
1976-01-01
An analysis of dynamic and nonlocal longitudinal dielectric response properties of a two-dimensional Landau-quantized plasma is carried out, using a thermodynamic Green's function formulation of the RPA with a two-dimensional thermal Green's function for electron propagation in a magnetic field developed in closed form. The longitudinal-electrostatic plasmon dispersion relation is discussed in the low wave-number regime with nonlocal corrections, and Bernstein mode structure is studied for arbitrary wavenumber. All regimes of magnetic field strength and statistics are investigated. The class of integrals treated here should have broad applicability in other two-dimensional and finite slab plasma studies.The two-dimensional static shielding law in a magnetic field is analyzed for low wavenumber, and for large distances we find V (r) approx. = Q/k 2 2 r 3 . The inverse screening length k 0 =2πe 2 partial rho/ partialxi (rho= density, xi= chemical potential) is evaluated in all regimes of magnetic field strength and all statistical regimes. k 0 exhibits violent DHVA oscillatory behavior in the degenerate zero-temperature case at higher field strengths, and the shielding is complete when xi =r'hω/subc/ but there is no shielding when xi does not = r'hω/subc/. A careful analysis confirms that there is no shielding at large distances in the degenerate quantum strong field limit h3π/subc/>xi. Since shielding does persist in the nondegenerate quantum strong field limit hω/subc/>KT, there should be a pronounced change in physical properties that depend on shielding if the system is driven through a high field statistical transition. Finally, we find that the zero field two-dimensional Friedel--Kohn ''wiggle'' static shielding phenomenon is destroyed by the dispersal of the zero field continuum of electron states into the discrete set of Landau-quantized orbitals due to the imposition of the magnetic field
Quantum stochastic calculus associated with quadratic quantum noises
International Nuclear Information System (INIS)
Ji, Un Cig; Sinha, Kalyan B.
2016-01-01
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus
Quantum stochastic calculus associated with quadratic quantum noises
Energy Technology Data Exchange (ETDEWEB)
Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju, Chungbuk 28644 (Korea, Republic of); Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in [Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore-64, India and Department of Mathematics, Indian Institute of Science, Bangalore-12 (India)
2016-02-15
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.
Universality of quantum gravity corrections.
Das, Saurya; Vagenas, Elias C
2008-11-28
We show that the existence of a minimum measurable length and the related generalized uncertainty principle (GUP), predicted by theories of quantum gravity, influence all quantum Hamiltonians. Thus, they predict quantum gravity corrections to various quantum phenomena. We compute such corrections to the Lamb shift, the Landau levels, and the tunneling current in a scanning tunneling microscope. We show that these corrections can be interpreted in two ways: (a) either that they are exceedingly small, beyond the reach of current experiments, or (b) that they predict upper bounds on the quantum gravity parameter in the GUP, compatible with experiments at the electroweak scale. Thus, more accurate measurements in the future should either be able to test these predictions, or further tighten the above bounds and predict an intermediate length scale between the electroweak and the Planck scale.
Three Solvable Matrix Models of a Quantum Catastrophe
Czech Academy of Sciences Publication Activity Database
Levai, G.; Růžička, František; Znojil, Miloslav
2014-01-01
Roč. 53, č. 9 (2014), s. 2875-2890 ISSN 0020-7748 Institutional support: RVO:61389005 Keywords : quantum theory * PT symmetry * Finite-dimensional non-Hermitian Hamiltonians * exceptional-point localization * quantum theory of catastrophes * methods of computer algebra Subject RIV: BE - Theoretical Physics Impact factor: 1.184, year: 2014
Quasi-integrability and two-dimensional QCD
International Nuclear Information System (INIS)
Abdalla, E.; Mohayaee, R.
1996-10-01
The notion of integrability in two-dimensional QCD is discussed. We show that in spite of an infinite number of conserved charges, particle production is not entirely suppressed. This phenomenon, which we call quasi-integrability, is explained in terms of quantum corrections to the combined algebra of higher-conserved and spectrum-generating currents. We predict the qualitative form of particle production probabilities and verify that they are in agreement with numerical data. We also discuss four-dimensional self-dual Yang-Mills theory in the light of our results. (author). 25 refs, 4 figs, 1 tab
Quantum vacuum energy in two dimensional space-times
International Nuclear Information System (INIS)
Davies, P.C.W.; Fulling, S.A.
1977-01-01
The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed. (author)
Quantum vacuum energy in two dimensional space-times
Energy Technology Data Exchange (ETDEWEB)
Davies, P C.W.; Fulling, S A [King' s Coll., London (UK). Dept. of Mathematics
1977-04-21
The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed.
Decay of homogeneous two-dimensional quantum turbulence
Baggaley, Andrew W.; Barenghi, Carlo F.
2018-03-01
We numerically simulate the free decay of two-dimensional quantum turbulence in a large, homogeneous Bose-Einstein condensate. The large number of vortices, the uniformity of the density profile, and the absence of boundaries (where vortices can drift out of the condensate) isolate the annihilation of vortex-antivortex pairs as the only mechanism which reduces the number of vortices, Nv, during the turbulence decay. The results clearly reveal that vortex annihilation is a four-vortex process, confirming the decay law Nv˜t-1 /3 where t is time, which was inferred from experiments with relatively few vortices in small harmonically trapped condensates.
One dimensional Dirac-Moshinsky oscillator-like system and isospectral partners
International Nuclear Information System (INIS)
Contreras-Astorga, A
2015-01-01
Two different exactly solvable systems are constructed using the supersymmetric quantum mechanics formalism and a pseudoscalar one-dimensional version of the Dirac- Moshinsky oscillator as a departing system. One system is built using a first-order SUSY transformation. The second is obtained through the confluent supersymmetry algorithm. The two of them are explicitly designed to have the same spectrum as the departing system and pseudoscalar potentials. (paper)
Jordan-Wigner fermionization and the theory of low-dimensional quantum spin models
International Nuclear Information System (INIS)
Derzhko, O.
2007-01-01
The idea of mapping quantum spin lattice model onto fermionic lattice model goes back to Jordan and Wigner (1928) who transformed s = 1/2 operators which commute at different lattice sites into fermionic operators. Later on the Jordan-Wigner transformation was used for mapping one-dimensional s = 1/2 isotropic XY (XX) model onto an exactly solvable tight-binding model of spinless fermions (Lieb, Schultz and Mattis, 1961). Since that times the Jordan-Wigner transformation is known as a powerful tool in the condensed matter theory especially in the theory of low-dimensional quantum spin systems. The aim of these lectures is to review the applications of the Jordan-Wigner fermionization technique for calculating dynamic properties of low-dimensional quantum spin models. The dynamic quantities (such as dynamic structure factors or dynamic susceptibilities) are observable directly or indirectly in various experiments. The frequency and wave-vector dependence of the dynamic quantities yields valuable information about the magnetic structure of materials. Owing to a tremendous recent progress in synthesizing low-dimensional magnetic materials detailed comparisons of theoretical results with direct experimental observation are becoming possible. The lectures are organized as follows. After a brief introduction of the Jordan-Wigner transformation for one-dimensional spin one half systems and some of its extensions for higher dimensions and higher spin values we focus on the dynamic properties of several low-dimensional quantum spin models. We start from a famous s = 1/2 XX chain. As a first step we recall well-known results for dynamics of the z-spin-component fluctuation operator and then turn to dynamics of the dimer and trimer fluctuation operators. The dynamics of the trimer fluctuations involves both the two fermion (one particle and one hole) and the four-fermion (two particles and two holes) excitations. We discuss some properties of the two-fermion and four
A conditionally exactly solvable generalization of the inverse square root potential
Energy Technology Data Exchange (ETDEWEB)
Ishkhanyan, A.M., E-mail: aishkhanyan@gmail.com [Institute for Physical Research, NAS of Armenia, Ashtarak 0203 (Armenia); Armenian State Pedagogical University, Yerevan 0010 (Armenia); Institute of Physics and Technology, National Research Tomsk Polytechnic University, Tomsk 634050 (Russian Federation)
2016-11-25
We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum. - Highlights: • We present a conditionally exactly solvable singular potential for 1D Schrödinger equation. • Each of the two fundamental solutions is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. • The exact equation for the energy spectrum is written using two Hermite functions that do not reduce to polynomials.
Exact wave functions of two-electron quantum rings.
Loos, Pierre-François; Gill, Peter M W
2012-02-24
We demonstrate that the Schrödinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational solutions can be found for any value of the angular momentum and that the singlet and triplet manifolds, which are degenerate, have distinct geometric phases. We also study the nodal structure associated with these two-electron states.
Beyond WKB quantum corrections to Hamilton-Jacobi theory
International Nuclear Information System (INIS)
Jurisch, Alexander
2007-01-01
In this paper, we develop quantum mechanics of quasi-one-dimensional systems upon the framework of the quantum-mechanical Hamilton-Jacobi theory. We will show that the Schroedinger point of view and the Hamilton-Jacobi point of view are fully equivalent in their description of physical systems, but differ in their descriptive manner. As a main result of this, a wavefunction in Hamilton-Jacobi theory can be decomposed into travelling waves in any point in space, not only asymptotically. Using the quasi-linearization technique, we derive quantum correction functions in every order of h-bar. The quantum correction functions will remove the turning-point singularity that plagues the WKB-series expansion already in zeroth order and thus provide an extremely good approximation to the full solution of the Schroedinger equation. In the language of quantum action it is also possible to elegantly solve the connection problem without asymptotic approximations. The use of quantum action further allows us to derive an equation by which the Maslov index is directly calculable without any approximations. Stationary quantum trajectories will also be considered and thoroughly discussed
Quantum error-correcting code for ternary logic
Majumdar, Ritajit; Basu, Saikat; Ghosh, Shibashis; Sur-Kolay, Susmita
2018-05-01
Ternary quantum systems are being studied because they provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the coefficient of one of the basis states is zero. Hence both (2 ×2 ) -dimensional and (3 ×3 ) -dimensional Pauli errors can occur on qutrits. In this paper, we (i) explore the possible (2 ×2 ) -dimensional as well as (3 ×3 ) -dimensional Pauli errors in qutrits and show that any pairwise bit swap error can be expressed as a linear combination of shift errors and phase errors, (ii) propose a special type of error called a quantum superposition error and show its equivalence to arbitrary rotation, (iii) formulate a nine-qutrit code which can correct a single error in a qutrit, and (iv) provide its stabilizer and circuit realization.
Non-relativistic quantum mechanics
Puri, Ravinder R
2017-01-01
This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...
Mixing times in quantum walks on two-dimensional grids
International Nuclear Information System (INIS)
Marquezino, F. L.; Portugal, R.; Abal, G.
2010-01-01
Mixing properties of discrete-time quantum walks on two-dimensional grids with toruslike boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and the running time of the corresponding abstract search algorithm is discussed.
Black holes in higher dimensional gravity theory with corrections quadratic in curvature
International Nuclear Information System (INIS)
Frolov, Valeri P.; Shapiro, Ilya L.
2009-01-01
Static spherically symmetric black holes are discussed in the framework of higher dimensional gravity with quadratic in curvature terms. Such terms naturally arise as a result of quantum corrections induced by quantum fields propagating in the gravitational background. We focus our attention on the correction of the form C 2 =C αβγδ C αβγδ . The Gauss-Bonnet equation in four-dimensional spacetime enables one to reduce this term in the action to the terms quadratic in the Ricci tensor and scalar curvature. As a result the Schwarzschild solution which is Ricci flat will be also a solution of the theory with the Weyl scalar C 2 correction. An important new feature of the spaces with dimension D>4 is that in the presence of the Weyl curvature-squared term a necessary solution differs from the corresponding 'classical' vacuum Tangherlini metric. This difference is related to the presence of secondary or induced hair. We explore how the Tangherlini solution is modified by 'quantum corrections', assuming that the gravitational radius r 0 is much larger than the scale of the quantum corrections. We also demonstrated that finding a general solution beyond the perturbation method can be reduced to solving a single third order ordinary differential equation (master equation).
Two-dimensional Yukawa interactions from nonlocal Proca quantum electrodynamics
Alves, Van Sérgio; Macrı, Tommaso; Magalhães, Gabriel C.; Marino, E. C.; Nascimento, Leandro O.
2018-05-01
We derive two versions of an effective model to describe dynamical effects of the Yukawa interaction among Dirac electrons in the plane. Such short-range interaction is obtained by introducing a mass term for the intermediate particle, which may be either scalar or an abelian gauge field, both of them in (3 +1 ) dimensions. Thereafter, we consider that the fermionic matter field propagates only in (2 +1 ) dimensions, whereas the bosonic field is free to propagate out of the plane. Within these assumptions, we apply a mechanism for dimensional reduction, which yields an effective model in (2 +1 ) dimensions. In particular, for the gauge-field case, we use the Stueckelberg mechanism in order to preserve gauge invariance. We refer to this version as nonlocal-Proca quantum electrodynamics (NPQED). For both scalar and gauge cases, the effective models reproduce the usual Yukawa interaction in the static limit. By means of perturbation theory at one loop, we calculate the mass renormalization of the Dirac field. Our model is a generalization of Pseudo quantum electrodynamics (PQED), which is a gauge-field model that provides a Coulomb interaction for two-dimensional electrons. Possibilities of application to Fermi-Bose mixtures in mixed dimensions, using cold atoms, are briefly discussed.
Quantum Fluctuations in Quasi-One-Dimensional Dipolar Bose-Einstein Condensates.
Edler, D; Mishra, C; Wächtler, F; Nath, R; Sinha, S; Santos, L
2017-08-04
Recent experiments have revealed that beyond-mean-field corrections are much more relevant in weakly interacting dipolar condensates than in their nondipolar counterparts. We show that in quasi-one-dimensional geometries quantum corrections in dipolar and nondipolar condensates are strikingly different due to the peculiar momentum dependence of the dipolar interactions. The energy correction of the condensate presents not only a modified density dependence, but it may even change from attractive to repulsive at a critical density due to the surprising role played by the transversal directions. The anomalous quantum correction translates into a strongly modified physics for quantum-stabilized droplets and dipolar solitons. Moreover, and for similar reasons, quantum corrections of three-body correlations, and hence of three-body losses, are strongly modified by the dipolar interactions. This intriguing physics can be readily probed in current experiments with magnetic atoms.
Stimulated wave of polarization in a one-dimensional Ising chain
International Nuclear Information System (INIS)
Lee, Jae-Seung; Khitrin, A.K.
2005-01-01
It is demonstrated that in a one-dimensional Ising chain with nearest-neighbor interactions, irradiated by a weak resonant transverse field, a stimulated wave of flipped spins can be triggered by a flip of a single spin. This analytically solvable model illustrates mechanisms of quantum amplification and quantum measurement
Detected-jump-error-correcting quantum codes, quantum error designs, and quantum computation
International Nuclear Information System (INIS)
Alber, G.; Mussinger, M.; Beth, Th.; Charnes, Ch.; Delgado, A.; Grassl, M.
2003-01-01
The recently introduced detected-jump-correcting quantum codes are capable of stabilizing qubit systems against spontaneous decay processes arising from couplings to statistically independent reservoirs. These embedded quantum codes exploit classical information about which qubit has emitted spontaneously and correspond to an active error-correcting code embedded in a passive error-correcting code. The construction of a family of one-detected-jump-error-correcting quantum codes is shown and the optimal redundancy, encoding, and recovery as well as general properties of detected-jump-error-correcting quantum codes are discussed. By the use of design theory, multiple-jump-error-correcting quantum codes can be constructed. The performance of one-jump-error-correcting quantum codes under nonideal conditions is studied numerically by simulating a quantum memory and Grover's algorithm
International Nuclear Information System (INIS)
Zduniak, A.; Dyakonov, M.I.; Litwin-Staszewska, E.; Knap, W.
1995-01-01
Week localization corrections to conductivity of two-dimensional electron gas are studied by measurements of magnetic field dependence of the conductivity in GaInAs quantum wells. We observed that, when presented as a function of the normalized magnetic field (x=B/B tr where B is the magnetic field, B tr =h/4eτD, D is the diffusion constant and τ is momentum relaxation time), different samples show very similar high field behaviour. A theoretical description is developed that allows one to describe in a consistent way and low field behaviour. The theory predicts universal (B -1/2 ) behaviour of the conductivity correction for all 2D systems in high field limit (x>1). Low field behaviour depends strongly on spin and phase relaxation mechanisms. Comparison of the theory with experiment confirms the universal behaviour in the high field limit and allows one to estimate the spin and phase relaxation times for different GaInAs quantum wells. (author)
Interaction of attosecond electromagnetic pulses with atoms: The exactly solvable model
International Nuclear Information System (INIS)
Popov, Yu. V.; Kouzakov, K. A.; Vinitsky, S. I.; Gusev, A. A.
2007-01-01
We consider the exactly solvable model of interaction of zero-duration electromagnetic pulses with an atom. The model has a number of peculiar properties which are outlined in the cases of a single pulse and two opposite pulses. In perspective, it can be useful in different fields of physics involving interaction of attosecond laser pulses with quantum systems
Quantum-critical scaling of fidelity in 2D pairing models
Energy Technology Data Exchange (ETDEWEB)
Adamski, Mariusz, E-mail: mariusz.adamski@ift.uni.wroc.pl [Institute of Theoretical Physics, University of Wrocław, pl. Maksa Borna 9, 50–204, Wrocław (Poland); Jȩdrzejewski, Janusz [Institute of Theoretical Physics, University of Wrocław, pl. Maksa Borna 9, 50–204, Wrocław (Poland); Krokhmalskii, Taras [Institute for Condensed Matter Physics, 1 Svientsitski Street, 79011, Lviv (Ukraine)
2017-01-15
The laws of quantum-critical scaling theory of quantum fidelity, dependent on the underlying system dimensionality D, have so far been verified in exactly solvable 1D models, belonging to or equivalent to interacting, quadratic (quasifree), spinless or spinfull, lattice-fermion models. The obtained results are so appealing that in quest for correlation lengths and associated universal critical indices ν, which characterize the divergence of correlation lengths on approaching critical points, one might be inclined to substitute the hard task of determining an asymptotic behavior at large distances of a two-point correlation function by an easier one, of determining the quantum-critical scaling of the quantum fidelity. However, the role of system's dimensionality has been left as an open problem. Our aim in this paper is to fill up this gap, at least partially, by verifying the laws of quantum-critical scaling theory of quantum fidelity in a 2D case. To this end, we study correlation functions and quantum fidelity of 2D exactly solvable models, which are interacting, quasifree, spinfull, lattice-fermion models. The considered 2D models exhibit new, as compared with 1D ones, features: at a given quantum-critical point there exists a multitude of correlation lengths and multiple universal critical indices ν, since these quantities depend on spatial directions, moreover, the indices ν may assume larger values. These facts follow from the obtained by us analytical asymptotic formulae for two-point correlation functions. In such new circumstances we discuss the behavior of quantum fidelity from the perspective of quantum-critical scaling theory. In particular, we are interested in finding out to what extent the quantum fidelity approach may be an alternative to the correlation-function approach in studies of quantum-critical points beyond 1D.
Alternate two-dimensional quantum walk with a single-qubit coin
International Nuclear Information System (INIS)
Di Franco, C.; Busch, Th.; Mc Gettrick, M.; Machida, T.
2011-01-01
We have recently proposed a two-dimensional quantum walk where the requirement of a higher dimensionality of the coin space is substituted with the alternance of the directions in which the walker can move [C. Di Franco, M. Mc Gettrick, and Th. Busch, Phys. Rev. Lett. 106, 080502 (2011)]. For a particular initial state of the coin, this walk is able to perfectly reproduce the spatial probability distribution of the nonlocalized case of the Grover walk. Here, we present a more detailed proof of this equivalence. We also extend the analysis to other initial states in order to provide a more complete picture of our walk. We show that this scheme outperforms the Grover walk in the generation of x-y spatial entanglement for any initial condition, with the maximum entanglement obtained in the case of the particular aforementioned state. Finally, the equivalence is generalized to wider classes of quantum walks and a limit theorem for the alternate walk in this context is presented.
Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes
Harrington, James William
Quantum information theory is concerned with identifying how quantum mechanical resources (such as entangled quantum states) can be utilized for a number of information processing tasks, including data storage, computation, communication, and cryptography. Efficient quantum algorithms and protocols have been developed for performing some tasks (e.g. , factoring large numbers, securely communicating over a public channel, and simulating quantum mechanical systems) that appear to be very difficult with just classical resources. In addition to identifying the separation between classical and quantum computational power, much of the theoretical focus in this field over the last decade has been concerned with finding novel ways of encoding quantum information that are robust against errors, which is an important step toward building practical quantum information processing devices. In this thesis I present some results on the quantum error-correcting properties of oscillator codes (also described as symplectic lattice codes) and toric codes. Any harmonic oscillator system (such as a mode of light) can be encoded with quantum information via symplectic lattice codes that are robust against shifts in the system's continuous quantum variables. I show the existence of lattice codes whose achievable rates match the one-shot coherent information over the Gaussian quantum channel. Also, I construct a family of symplectic self-dual lattices and search for optimal encodings of quantum information distributed between several oscillators. Toric codes provide encodings of quantum information into two-dimensional spin lattices that are robust against local clusters of errors and which require only local quantum operations for error correction. Numerical simulations of this system under various error models provide a calculation of the accuracy threshold for quantum memory using toric codes, which can be related to phase transitions in certain condensed matter models. I also present
Quantum error correction for beginners
International Nuclear Information System (INIS)
Devitt, Simon J; Nemoto, Kae; Munro, William J
2013-01-01
Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspects of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large-scale quantum computers. The introduction of quantum error correction in 1995 showed that active techniques could be employed to mitigate this fatal problem. However, quantum error correction and fault-tolerant computation is now a much larger field and many new codes, techniques, and methodologies have been developed to implement error correction for large-scale quantum algorithms. In response, we have attempted to summarize the basic aspects of quantum error correction and fault-tolerance, not as a detailed guide, but rather as a basic introduction. The development in this area has been so pronounced that many in the field of quantum information, specifically researchers who are new to quantum information or people focused on the many other important issues in quantum computation, have found it difficult to keep up with the general formalisms and methodologies employed in this area. Rather than introducing these concepts from a rigorous mathematical and computer science framework, we instead examine error correction and fault-tolerance largely through detailed examples, which are more relevant to experimentalists today and in the near future. (review article)
Exotic ferromagnetism in the two-dimensional quantum material C3N
Huang, Wen-Cheng; Li, Wei; Liu, Xiaosong
2018-04-01
The search for and study of exotic quantum states in novel low-dimensional quantum materials have triggered extensive research in recent years. Here, we systematically study the electronic and magnetic structures in the newly discovered two-dimensional quantum material C3N within the framework of density functional theory. The calculations demonstrate that C3N is an indirect-band semiconductor with an energy gap of 0.38 eV, which is in good agreement with experimental observations. Interestingly, we find van Hove singularities located at energies near the Fermi level, which is half that of graphene. Thus, the Fermi energy easily approaches that of the singularities, driving the system to ferromagnetism, under charge carrier injection, such as electric field gating or hydrogen doping. These findings not only demonstrate that the emergence of magnetism stems from the itinerant electron mechanism rather than the effects of local magnetic impurities, but also open a new avenue to designing field-effect transistor devices for possible realization of an insulator-ferromagnet transition by tuning an external electric field.
Czech Academy of Sciences Publication Activity Database
Kiguradze, I.; Šremr, Jiří
2011-01-01
Roč. 74, č. 17 (2011), s. 6537-6552 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear differential system * non-local boundary value problem * solvability Subject RIV: BA - General Mathematics Impact factor: 1.536, year: 2011 http://www.sciencedirect.com/science/article/pii/S0362546X11004573
Two-dimensional distributed-phase-reference protocol for quantum key distribution
DEFF Research Database (Denmark)
Bacco, Davide; Christensen, Jesper Bjerge; Usuga Castaneda, Mario A.
2016-01-01
10 years, long-distance fiber-based DPR systems have been successfully demonstrated, although fundamental obstacles such as intrinsic channel losses limit their performance. Here, we introduce the first two-dimensional DPR-QKD protocol in which information is encoded in the time and phase of weak......Quantum key distribution (QKD) and quantum communication enable the secure exchange of information between remote parties. Currently, the distributed-phase-reference (DPR) protocols, which are based on weak coherent pulses, are among the most practical solutions for long-range QKD. During the last...... coherent pulses. The ability of extracting two bits of information per detection event, enables a higher secret key rate in specific realistic network scenarios. Moreover, despite the use of more dimensions, the proposed protocol remains simple, practical, and fully integrable....
Two-dimensional distributed-phase-reference protocol for quantum key distribution
Bacco, Davide; Christensen, Jesper Bjerge; Castaneda, Mario A. Usuga; Ding, Yunhong; Forchhammer, Søren; Rottwitt, Karsten; Oxenløwe, Leif Katsuo
2016-12-01
Quantum key distribution (QKD) and quantum communication enable the secure exchange of information between remote parties. Currently, the distributed-phase-reference (DPR) protocols, which are based on weak coherent pulses, are among the most practical solutions for long-range QKD. During the last 10 years, long-distance fiber-based DPR systems have been successfully demonstrated, although fundamental obstacles such as intrinsic channel losses limit their performance. Here, we introduce the first two-dimensional DPR-QKD protocol in which information is encoded in the time and phase of weak coherent pulses. The ability of extracting two bits of information per detection event, enables a higher secret key rate in specific realistic network scenarios. Moreover, despite the use of more dimensions, the proposed protocol remains simple, practical, and fully integrable.
Few quantum particles on one dimensional lattices
Energy Technology Data Exchange (ETDEWEB)
Valiente Cifuentes, Manuel
2010-06-18
There is currently a great interest in the physics of degenerate quantum gases and low-energy few-body scattering due to the recent experimental advances in manipulation of ultracold atoms by light. In particular, almost perfect periodic potentials, called optical lattices, can be generated. The lattice spacing is fixed by the wavelength of the laser field employed and the angle betwen the pair of laser beams; the lattice depth, defining the magnitude of the different band gaps, is tunable within a large interval of values. This flexibility permits the exploration of different regimes, ranging from the ''free-electron'' picture, modified by the effective mass for shallow optical lattices, to the tight-binding regime of a very deep periodic potential. In the latter case, effective single-band theories, widely used in condensed matter physics, can be implemented with unprecedent accuracy. The tunability of the lattice depth is nowadays complemented by the use of magnetic Feshbach resonances which, at very low temperatures, can vary the relevant atom-atom scattering properties at will. Moreover, optical lattices loaded with gases of effectively reduced dimensionality are experimentally accessible. This is especially important for one spatial dimension, since most of the exactly solvable models in many-body quantum mechanics deal with particles on a line; therefore, experiments with one-dimensional gases serve as a testing ground for many old and new theories which were regarded as purely academic not so long ago. The physics of few quantum particles on a one-dimensional lattice is the topic of this thesis. Most of the results are obtained in the tight-binding approximation, which is amenable to exact numerical or analytical treatment. For the two-body problem, theoretical methods for calculating the stationary scattering and bound states are developed. These are used to obtain, in closed form, the two-particle solutions of both the Hubbard and
Few quantum particles on one dimensional lattices
International Nuclear Information System (INIS)
Valiente Cifuentes, Manuel
2010-01-01
There is currently a great interest in the physics of degenerate quantum gases and low-energy few-body scattering due to the recent experimental advances in manipulation of ultracold atoms by light. In particular, almost perfect periodic potentials, called optical lattices, can be generated. The lattice spacing is fixed by the wavelength of the laser field employed and the angle betwen the pair of laser beams; the lattice depth, defining the magnitude of the different band gaps, is tunable within a large interval of values. This flexibility permits the exploration of different regimes, ranging from the ''free-electron'' picture, modified by the effective mass for shallow optical lattices, to the tight-binding regime of a very deep periodic potential. In the latter case, effective single-band theories, widely used in condensed matter physics, can be implemented with unprecedent accuracy. The tunability of the lattice depth is nowadays complemented by the use of magnetic Feshbach resonances which, at very low temperatures, can vary the relevant atom-atom scattering properties at will. Moreover, optical lattices loaded with gases of effectively reduced dimensionality are experimentally accessible. This is especially important for one spatial dimension, since most of the exactly solvable models in many-body quantum mechanics deal with particles on a line; therefore, experiments with one-dimensional gases serve as a testing ground for many old and new theories which were regarded as purely academic not so long ago. The physics of few quantum particles on a one-dimensional lattice is the topic of this thesis. Most of the results are obtained in the tight-binding approximation, which is amenable to exact numerical or analytical treatment. For the two-body problem, theoretical methods for calculating the stationary scattering and bound states are developed. These are used to obtain, in closed form, the two-particle solutions of both the Hubbard and extended Hubbard models
International Nuclear Information System (INIS)
Taboryski, R.; Veje, E.; Lindelof, P.E.
1990-01-01
Magnetoresistance with the field perpendicular to the 2-dimensional electron gas in a high mobility GaAs/AlGaAs heterostructure at low temperatures is studied. At the lowest magnetic field we observe the weak localization. At magnetic fields, where the product of the mobility and the magnetic field is of the order of unity, the quantum correction to conductivity due to the electron-electron interaction is as a source of magnetoresistance. A consistent analysis of experiments in this regime is for the first time performed. In addition to the well known electron-electron term with the expected temperature dependence, we find a new type of temperature independent quantum correction, which varies logarithmically with mobility. (orig.)
Strong chaos in one-dimensional quantum system
International Nuclear Information System (INIS)
Yang, C.-D.; Wei, C.-H.
2008-01-01
According to the Poincare-Bendixson theorem, a minimum of three autonomous equations is required to exhibit deterministic chaos. Because a one-dimensional quantum system is described by only two autonomous equations using de Broglie-Bohm's trajectory interpretation, chaos in one-dimensional quantum systems has long been considered impossible. We will prove in this paper that chaos phenomenon does exist in one-dimensional quantum systems, if the domain of quantum motions is extended to complex space by noting that the quantum world is actually characterized by a four-dimensional complex spacetime according to the E (∞) theory. Furthermore, we point out that the interaction between the real and imaginary parts of complex trajectories produces a new chaos phenomenon unique to quantum systems, called strong chaos, which describes the situation that quantum trajectories may emerge and diverge spontaneously without any perturbation in the initial position
Test of quantum thermalization in the two-dimensional transverse-field Ising model.
Blaß, Benjamin; Rieger, Heiko
2016-12-01
We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems.
Vinci, Walter; Lidar, Daniel A.
2018-02-01
Nested quantum annealing correction (NQAC) is an error-correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. The encoding replaces each logical qubit by a complete graph of degree C . The nesting level C represents the distance of the error-correcting code and controls the amount of protection against thermal and control errors. Theoretical mean-field analyses and empirical data obtained with a D-Wave Two quantum annealer (supporting up to 512 qubits) showed that NQAC has the potential to achieve a scalable effective-temperature reduction, Teff˜C-η , with 0 temperature of a quantum annealer. Such effective-temperature reduction is relevant for machine-learning applications. Since we demonstrate that NQAC achieves error correction via a reduction of the effective-temperature of the quantum annealing device, our results address the problem of the "temperature scaling law for quantum annealers," which requires the temperature of quantum annealers to be reduced as problems of larger sizes are attempted to be solved.
Supersymmetric construction of exactly solvable potentials and nonlinear algebras
International Nuclear Information System (INIS)
Junker, G.; Roy, P.
1998-01-01
Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and lowering operators of these harmonic oscillators and the SUSY operators we construct ladder operators for these new conditionally solvable systems. It is found that these ladder operators together with the Hamilton operator form a nonlinear algebra which is of quadratic and cubic type for the SUSY partners of the linear and radial harmonic oscillator
Leading quantum gravitational corrections to scalar QED
International Nuclear Information System (INIS)
Bjerrum-Bohr, N.E.J.
2002-01-01
We consider the leading post-Newtonian and quantum corrections to the non-relativistic scattering amplitude of charged scalars in the combined theory of general relativity and scalar QED. The combined theory is treated as an effective field theory. This allows for a consistent quantization of the gravitational field. The appropriate vertex rules are extracted from the action, and the non-analytic contributions to the 1-loop scattering matrix are calculated in the non-relativistic limit. The non-analytical parts of the scattering amplitude, which are known to give the long range, low energy, leading quantum corrections, are used to construct the leading post-Newtonian and quantum corrections to the two-particle non-relativistic scattering matrix potential for two charged scalars. The result is discussed in relation to experimental verifications
Quantum glassiness in clean strongly correlated systems: an example of topological overprotection
Chamon, Claudio
2005-03-01
Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath. However, this paradigm breaks down if thermal equilibration is obstructed. I present solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, 1) have no quenched disorder, 2) have solely local interactions, 3) have an exactly solvable spectrum, 4) have topologically ordered ground states, and 5) have slow dynamical relaxation rates akin to those of strong structural glasses.
On a family of (1+1)-dimensional scalar field theory models: Kinks, stability, one-loop mass shifts
Energy Technology Data Exchange (ETDEWEB)
Alonso-Izquierdo, A., E-mail: alonsoiz@usal.es [Departamento de Matematica Aplicada and IUFFyM, Universidad de Salamanca (Spain); Mateos Guilarte, J. [Departamento de Fisica Fundamental and IUFFyM, Universidad de Salamanca (Spain)
2012-09-15
In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and {phi}{sup 4} models, we look at all possible extensions such that the kink second-order fluctuation operators are Schroedinger differential operators with Poeschl-Teller potential wells. In this situation, the associated spectral problem is solvable and therefore we shall succeed in analyzing the kink stability completely and in computing the one-loop quantum correction to the kink mass exactly. When the parameter is a natural number, the family becomes the hierarchy for which the potential wells are reflectionless, the two first levels of the hierarchy being the sine-Gordon and {phi}{sup 4} models. - Highlights: Black-Right-Pointing-Pointer We construct a family of scalar field theory models supporting kinks. Black-Right-Pointing-Pointer The second-order kink fluctuation operators involve Poeschl-Teller potential wells. Black-Right-Pointing-Pointer We compute the one-loop quantum correction to the kink mass with different methods.
Towards self-correcting quantum memories
Michnicki, Kamil
This thesis presents a model of self-correcting quantum memories where quantum states are encoded using topological stabilizer codes and error correction is done using local measurements and local dynamics. Quantum noise poses a practical barrier to developing quantum memories. This thesis explores two types of models for suppressing noise. One model suppresses thermalizing noise energetically by engineering a Hamiltonian with a high energy barrier between code states. Thermalizing dynamics are modeled phenomenologically as a Markovian quantum master equation with only local generators. The second model suppresses stochastic noise with a cellular automaton that performs error correction using syndrome measurements and a local update rule. Several ways of visualizing and thinking about stabilizer codes are presented in order to design ones that have a high energy barrier: the non-local Ising model, the quasi-particle graph and the theory of welded stabilizer codes. I develop the theory of welded stabilizer codes and use it to construct a code with the highest known energy barrier in 3-d for spin Hamiltonians: the welded solid code. Although the welded solid code is not fully self correcting, it has some self correcting properties. It has an increased memory lifetime for an increased system size up to a temperature dependent maximum. One strategy for increasing the energy barrier is by mediating an interaction with an external system. I prove a no-go theorem for a class of Hamiltonians where the interaction terms are local, of bounded strength and commute with the stabilizer group. Under these conditions the energy barrier can only be increased by a multiplicative constant. I develop cellular automaton to do error correction on a state encoded using the toric code. The numerical evidence indicates that while there is no threshold, the model can extend the memory lifetime significantly. While of less theoretical importance, this could be practical for real
Itinerant quantum multicriticality of two-dimensional Dirac fermions
Roy, Bitan; Goswami, Pallab; Juričić, Vladimir
2018-05-01
We analyze emergent quantum multicriticality for strongly interacting, massless Dirac fermions in two spatial dimensions (d =2 ) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break O(S1) and O(S2) symmetries in the ordered phase. Performing a renormalization-group analysis by using the ɛ =(3 -d ) expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an enlarged O(S1+S2) chiral symmetry. Such a fixed point acts as an exotic quantum multicritical point (MCP), governing the continuous semimetal-insulator as well as insulator-insulator (for example, antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either O(S1) or O(S2) chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power-law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher-dimensional Dirac fermions is also outlined.
Degenerate ground states and multiple bifurcations in a two-dimensional q-state quantum Potts model.
Dai, Yan-Wei; Cho, Sam Young; Batchelor, Murray T; Zhou, Huan-Qiang
2014-06-01
We numerically investigate the two-dimensional q-state quantum Potts model on the infinite square lattice by using the infinite projected entangled-pair state (iPEPS) algorithm. We show that the quantum fidelity, defined as an overlap measurement between an arbitrary reference state and the iPEPS ground state of the system, can detect q-fold degenerate ground states for the Z_{q} broken-symmetry phase. Accordingly, a multiple bifurcation of the quantum ground-state fidelity is shown to occur as the transverse magnetic field varies from the symmetry phase to the broken-symmetry phase, which means that a multiple-bifurcation point corresponds to a critical point. A (dis)continuous behavior of quantum fidelity at phase transition points characterizes a (dis)continuous phase transition. Similar to the characteristic behavior of the quantum fidelity, the magnetizations, as order parameters, obtained from the degenerate ground states exhibit multiple bifurcation at critical points. Each order parameter is also explicitly demonstrated to transform under the Z_{q} subgroup of the symmetry group of the Hamiltonian. We find that the q-state quantum Potts model on the square lattice undergoes a discontinuous (first-order) phase transition for q=3 and q=4 and a continuous phase transition for q=2 (the two-dimensional quantum transverse Ising model).
Energy Technology Data Exchange (ETDEWEB)
Zduniak, A.; Dyakonov, M.I.; Litwin-Staszewska, E.; Knap, W. [Groupe d`Etudes des Semiconducteurs, Universite de Montpellier II, Montpellier (France)
1995-12-31
Week localization corrections to conductivity of two-dimensional electron gas are studied by measurements of magnetic field dependence of the conductivity in GaInAs quantum wells. We observed that, when presented as a function of the normalized magnetic field (x=B/B{sub tr} where B is the magnetic field, B{sub tr}=h/4e{tau}D, D is the diffusion constant and {tau} is momentum relaxation time), different samples show very similar high field behaviour. A theoretical description is developed that allows one to describe in a consistent way and low field behaviour. The theory predicts universal (B{sup -1/2}) behaviour of the conductivity correction for all 2D systems in high field limit (x>1). Low field behaviour depends strongly on spin and phase relaxation mechanisms. Comparison of the theory with experiment confirms the universal behaviour in the high field limit and allows one to estimate the spin and phase relaxation times for different GaInAs quantum wells. (author). 5 refs, 2 figs.
Parametric study of nonlinear electrostatic waves in two-dimensional quantum dusty plasmas
International Nuclear Information System (INIS)
Ali, S; Moslem, W M; Kourakis, I; Shukla, P K
2008-01-01
The nonlinear properties of two-dimensional cylindrical quantum dust-ion-acoustic (QDIA) and quantum dust-acoustic (QDA) waves are studied in a collisionless, unmagnetized and dense (quantum) dusty plasma. For this purpose, the reductive perturbation technique is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining the cylindrical Kadomtsev-Petviashvili (CKP) equations. The effects of quantum diffraction, as well as quantum statistical and geometric effects on the profiles of QDIA and QDA solitary waves are examined. It is found that the amplitudes and widths of the nonplanar QDIA and QDA waves are significantly affected by the quantum electron tunneling effect. The addition of a dust component to a quantum plasma is seen to affect the propagation characteristics of localized QDIA excitations. In the case of low-frequency QDA waves, this effect is even stronger, since the actual form of the potential solitary waves, in fact, depends on the dust charge polarity (positive/negative) itself (allowing for positive/negative potential forms, respectively). The relevance of the present investigation to metallic nanostructures is highlighted
New rational extensions of solvable potentials with finite bound state spectrum
International Nuclear Information System (INIS)
Grandati, Yves
2012-01-01
Using the disconjugacy properties of the Schrödinger equation, we develop a new type of generalized SUSY QM partnership which allows generating new solvable rational extensions for translationally shape invariant potentials having a finite bound state spectrum. For this we prolong the dispersion relation relating the energy to the quantum number out of the physical domain until a disconjugacy sector. By Darboux–Bäcklund Transformations built on these prolonged states we obtain new regular isospectral extensions of the initial potential. We give the spectra of these extensions in terms of new orthogonal polynomials and study their shape invariance properties. -- Highlights: ► New solvable quantum potentials. ► SUSY quantum partnership generalized to excited states. ► Based on disconjugacy theorems and asymptotic behaviour. ► Exact spectrum in terms of new orthogonal polynomials. ► Enlarged shape invariance property.
Quantum-mechanical scattering in one dimension
International Nuclear Information System (INIS)
Boya, Luis J.
2008-01-01
The purpose of this mainly pedagogical review is to fill a lacuna in the usual treatment of scattering in quantum mechanics, by showing the essential of it in the simplest, one-dimensional setting. We define in this situation amplitudes and scattering coefficients and deal with optical and Levinson' theorems as consequences of unitarity in coordinate or momentum space. Parity waves en lieu of partial waves, integral equations and Born series, etc., are defined naturally in this frame. Several solvable examples are shown. Two topics best studied in 1d are transparent potentials and supersymmetric quantum mechanics. Elementary analytical properties and general behaviour of amplitudes give rise to study inverse problems, that is, recovering the potential from scattering data. Isospectral deformations of the wave equation give relations with some nonlinear evolution equations (Lax), solvable by the inverse scattering method (Kruskal), and we consider the KdV equation as an example. We also refer briefly to some singular potentials, where, e.g., the essence of renormalization can be read off again in the simplest setting. The whole paper emphasizes the tutorial and introductory aspects
Test of quantum thermalization in the two-dimensional transverse-field Ising model
Blaß, Benjamin; Rieger, Heiko
2016-01-01
We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems. PMID:27905523
DEFF Research Database (Denmark)
Lassen, Mikael Østergaard; Sabuncu, Metin; Huck, Alexander
2010-01-01
A fundamental requirement for enabling fault-tolerant quantum information processing is an efficient quantum error-correcting code that robustly protects the involved fragile quantum states from their environment. Just as classical error-correcting codes are indispensible in today's information...... technologies, it is believed that quantum error-correcting code will play a similarly crucial role in tomorrow's quantum information systems. Here, we report on the experimental demonstration of a quantum erasure-correcting code that overcomes the devastating effect of photon losses. Our quantum code is based...... on linear optics, and it protects a four-mode entangled mesoscopic state of light against erasures. We investigate two approaches for circumventing in-line losses, and demonstrate that both approaches exhibit transmission fidelities beyond what is possible by classical means. Because in-line attenuation...
First-principles engineering of charged defects for two-dimensional quantum technologies
Wu, Feng; Galatas, Andrew; Sundararaman, Ravishankar; Rocca, Dario; Ping, Yuan
2017-12-01
Charged defects in two-dimensional (2D) materials have emerging applications in quantum technologies such as quantum emitters and quantum computation. The advancement of these technologies requires a rational design of ideal defect centers, demanding reliable computation methods for the quantitatively accurate prediction of defect properties. We present an accurate, parameter-free, and efficient procedure to evaluate the quasiparticle defect states and thermodynamic charge transition levels of defects in 2D materials. Importantly, we solve critical issues that stem from the strongly anisotropic screening in 2D materials, that have so far precluded the accurate prediction of charge transition levels in these materials. Using this procedure, we investigate various defects in monolayer hexagonal boron nitride (h -BN ) for their charge transition levels, stable spin states, and optical excitations. We identify CBVN (nitrogen vacancy adjacent to carbon substitution of boron) to be the most promising defect candidate for scalable quantum bit and emitter applications.
Dimensional reduction in quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Hooft, G [Rijksuniversiteit Utrecht (Netherlands). Inst. voor Theoretische Fysica
1994-12-31
The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable degrees of freedom can best be described as if they were Boolean variables defined on a two- dimensional lattice, evolving with time. This observation, deduced from not much more than unitarity, entropy and counting arguments, implies severe restrictions on possible models of quantum gravity. Using cellular automata as an example it is argued that this dimensional reduction implies more constraints than the freedom we have in constructing models. This is the main reason why so-far no completely consistent mathematical models of quantum black holes have been found. (author). 13 refs, 2 figs.
Quantum corrections to Bekenstein–Hawking black hole entropy and gravity partition functions
International Nuclear Information System (INIS)
Bytsenko, A.A.; Tureanu, A.
2013-01-01
Algebraic aspects of the computation of partition functions for quantum gravity and black holes in AdS 3 are discussed. We compute the sub-leading quantum corrections to the Bekenstein–Hawking entropy. It is shown that the quantum corrections to the classical result can be included systematically by making use of the comparison with conformal field theory partition functions, via the AdS 3 /CFT 2 correspondence. This leads to a better understanding of the role of modular and spectral functions, from the point of view of the representation theory of infinite-dimensional Lie algebras. Besides, the sum of known quantum contributions to the partition function can be presented in a closed form, involving the Patterson–Selberg spectral function. These contributions can be reproduced in a holomorphically factorized theory whose partition functions are associated with the formal characters of the Virasoro modules. We propose a spectral function formulation for quantum corrections to the elliptic genus from supergravity states
Open quantum systems and error correction
Shabani Barzegar, Alireza
Quantum effects can be harnessed to manipulate information in a desired way. Quantum systems which are designed for this purpose are suffering from harming interaction with their surrounding environment or inaccuracy in control forces. Engineering different methods to combat errors in quantum devices are highly demanding. In this thesis, I focus on realistic formulations of quantum error correction methods. A realistic formulation is the one that incorporates experimental challenges. This thesis is presented in two sections of open quantum system and quantum error correction. Chapters 2 and 3 cover the material on open quantum system theory. It is essential to first study a noise process then to contemplate methods to cancel its effect. In the second chapter, I present the non-completely positive formulation of quantum maps. Most of these results are published in [Shabani and Lidar, 2009b,a], except a subsection on geometric characterization of positivity domain of a quantum map. The real-time formulation of the dynamics is the topic of the third chapter. After introducing the concept of Markovian regime, A new post-Markovian quantum master equation is derived, published in [Shabani and Lidar, 2005a]. The section of quantum error correction is presented in three chapters of 4, 5, 6 and 7. In chapter 4, we introduce a generalized theory of decoherence-free subspaces and subsystems (DFSs), which do not require accurate initialization (published in [Shabani and Lidar, 2005b]). In Chapter 5, we present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the encoding, recovery, or both, and is amenable to approximations that significantly improve computational cost while retaining fidelity (see [Kosut et al., 2008] for a published version). Chapter 6 is devoted to a theory of quantum error correction (QEC
The Conical Singularity and Quantum Corrections to Entropy of Black Hole
International Nuclear Information System (INIS)
Solodukhin, S.N.
1994-01-01
It is well known that at the temperature different from the Hawking temperature there appears a conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by regular surface is used to determine the curvature tensors for such metrics. It allows to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional and four-dimensional cases are considered. The entropy of the Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions. It corresponds to the results obtained earlier. For the eternal 2D black hole we observe finite, dependent on the mass, correction to the entropy. The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison to the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole. We argue that infinities of the entropy in four dimensions are renormalized with the renormalization of the gravitational coupling. (author). 35 refs
Quantum diffusion in two-dimensional random systems with particle–hole symmetry
International Nuclear Information System (INIS)
Ziegler, K
2012-01-01
We study the scattering dynamics of an n-component spinor wavefunction in a random environment on a two-dimensional lattice. If the particle–hole symmetry of the Hamiltonian is spontaneously broken the dynamics of the quantum particles becomes diffusive on large scales. The latter is described by a non-interacting Grassmann field, indicating a special kind of asymptotic freedom on large scales in d = 2. (paper)
Quantum Error Correction and Fault Tolerant Quantum Computing
Gaitan, Frank
2008-01-01
It was once widely believed that quantum computation would never become a reality. However, the discovery of quantum error correction and the proof of the accuracy threshold theorem nearly ten years ago gave rise to extensive development and research aimed at creating a working, scalable quantum computer. Over a decade has passed since this monumental accomplishment yet no book-length pedagogical presentation of this important theory exists. Quantum Error Correction and Fault Tolerant Quantum Computing offers the first full-length exposition on the realization of a theory once thought impo
NP-hardness of decoding quantum error-correction codes
Hsieh, Min-Hsiu; Le Gall, François
2011-05-01
Although the theory of quantum error correction is intimately related to classical coding theory and, in particular, one can construct quantum error-correction codes (QECCs) from classical codes with the dual-containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expects degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or nondegenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.
NP-hardness of decoding quantum error-correction codes
International Nuclear Information System (INIS)
Hsieh, Min-Hsiu; Le Gall, Francois
2011-01-01
Although the theory of quantum error correction is intimately related to classical coding theory and, in particular, one can construct quantum error-correction codes (QECCs) from classical codes with the dual-containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expects degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or nondegenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.
Quantum matrices in two dimensions
International Nuclear Information System (INIS)
Ewen, H.; Ogievetsky, O.; Wess, J.
1991-01-01
Quantum matrices in two-dimensions, admitting left and right quantum spaces, are classified: they fall into two families, the 2-parametric family GL p,q (2) and a 1-parametric family GL α J (2). Phenomena previously found for GL p,q (2) hold in this general situation: (a) powers of quantum matrices are again quantum and (b) entries of the logarithm of a two-dimensional quantum matrix form a Lie algebra. (orig.)
Higher (odd dimensional quantum Hall effect and extended dimensional hierarchy
Directory of Open Access Journals (Sweden)
Kazuki Hasebe
2017-07-01
Full Text Available We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S2k−1 in the SO(2k−1 monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S2k−1 to the one-dimension higher SO(2k gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah–Patodi–Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.
Czech Academy of Sciences Publication Activity Database
Znojil, Miloslav
2013-01-01
Roč. 336, SEP (2013), s. 98-111 ISSN 0003-4916 R&D Projects: GA ČR GAP203/11/1433 Institutional support: RVO:61389005 Keywords : Non-Hermitian quantum Hamiltonian * exceptional point * phase transition * exactly solvable model Subject RIV: BE - Theoretical Physics Impact factor: 3.065, year: 2013 http://www.sciencedirect.com/science/article/pii/S0003491613001267
Quantum algorithms and quantum maps - implementation and error correction
International Nuclear Information System (INIS)
Alber, G.; Shepelyansky, D.
2005-01-01
Full text: We investigate the dynamics of the quantum tent map under the influence of errors and explore the possibilities of quantum error correcting methods for the purpose of stabilizing this quantum algorithm. It is known that static but uncontrollable inter-qubit couplings between the qubits of a quantum information processor lead to a rapid Gaussian decay of the fidelity of the quantum state. We present a new error correcting method which slows down this fidelity decay to a linear-in-time exponential one. One of its advantages is that it does not require redundancy so that all physical qubits involved can be used for logical purposes. We also study the influence of decoherence due to spontaneous decay processes which can be corrected by quantum jump-codes. It is demonstrated how universal encoding can be performed in these code spaces. For this purpose we discuss a new entanglement gate which can be used for lowest level encoding in concatenated error-correcting architectures. (author)
Two dimensional kicked quantum Ising model: dynamical phase transitions
International Nuclear Information System (INIS)
Pineda, C; Prosen, T; Villaseñor, E
2014-01-01
Using an efficient one and two qubit gate simulator operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin 1/2 model on a two-dimensional lattice, which is periodically driven by a δ-pulsed transverse magnetic field. We consider three different dynamical properties: (i) level density, (ii) level spacing distribution of the Floquet quasienergy spectrum, and (iii) time-averaged autocorrelation function of magnetization components. Varying the parameters of the model, we found transitions between ordered (non-ergodic) and quantum chaotic (ergodic) phases, but the transitions between flat and non-flat spectral density do not correspond to transitions between ergodic and non-ergodic local observables. Even more surprisingly, we found good agreement of level spacing distribution with the Wigner surmise of random matrix theory for almost all values of parameters except where the model is essentially non-interacting, even in regions where local observables are not ergodic or where spectral density is non-flat. These findings question the versatility of the interpretation of level spacing distribution in many-body systems and stress the importance of the concept of locality. (paper)
Magnetoresistance in two-dimensional array of Ge/Si quantum dots
Stepina, N. P.; Koptev, E. S.; Pogosov, A. G.; Dvurechenskii, A. V.; Nikiforov, A. I.; Zhdanov, E. Yu
2012-07-01
Magnetoresistance in two-dimensional array of Ge/Si was studied for a wide range of the conductance, where the transport regime changes from hopping to diffusive one. The behavior of magnetoresistance is similar for all samples; it is negative in weak fields and becomes positive with increasing of magnetic field. Negative magnetoresistance can be described in the frame of weak localization approach with suggestion that quantum interference contribution to the conductance is restricted not only by the phase breaking length but also by the localization length.
Magnetoresistance in two-dimensional array of Ge/Si quantum dots
International Nuclear Information System (INIS)
Stepina, N P; Koptev, E S; Pogosov, A G; Dvurechenskii, A V; Nikiforov, A I; Zhdanov, E Yu
2012-01-01
Magnetoresistance in two-dimensional array of Ge/Si was studied for a wide range of the conductance, where the transport regime changes from hopping to diffusive one. The behavior of magnetoresistance is similar for all samples; it is negative in weak fields and becomes positive with increasing of magnetic field. Negative magnetoresistance can be described in the frame of weak localization approach with suggestion that quantum interference contribution to the conductance is restricted not only by the phase breaking length but also by the localization length.
Topics in quantum cryptography, quantum error correction, and channel simulation
Luo, Zhicheng
In this thesis, we mainly investigate four different topics: efficiently implementable codes for quantum key expansion [51], quantum error-correcting codes based on privacy amplification [48], private classical capacity of quantum channels [44], and classical channel simulation with quantum side information [49, 50]. For the first topic, we propose an efficiently implementable quantum key expansion protocol, capable of increasing the size of a pre-shared secret key by a constant factor. Previously, the Shor-Preskill proof [64] of the security of the Bennett-Brassard 1984 (BB84) [6] quantum key distribution protocol relied on the theoretical existence of good classical error-correcting codes with the "dual-containing" property. But the explicit and efficiently decodable construction of such codes is unknown. We show that we can lift the dual-containing constraint by employing the non-dual-containing codes with excellent performance and efficient decoding algorithms. For the second topic, we propose a construction of Calderbank-Shor-Steane (CSS) [19, 68] quantum error-correcting codes, which are originally based on pairs of mutually dual-containing classical codes, by combining a classical code with a two-universal hash function. We show, using the results of Renner and Koenig [57], that the communication rates of such codes approach the hashing bound on tensor powers of Pauli channels in the limit of large block-length. For the third topic, we prove a regularized formula for the secret key assisted capacity region of a quantum channel for transmitting private classical information. This result parallels the work of Devetak on entanglement assisted quantum communication capacity. This formula provides a new family protocol, the private father protocol, under the resource inequality framework that includes the private classical communication without the assisted secret keys as a child protocol. For the fourth topic, we study and solve the problem of classical channel
Ellison, Mark D.
2008-01-01
The one-dimensional particle-in-a-box model used to introduce quantum mechanics to students suffers from a tenuous connection to a real physical system. This article presents a two-dimensional model, the particle confined within a ring, that directly corresponds to observations of surface electrons in a metal trapped inside a circular barrier.…
Controlled teleportation of a 3-dimensional bipartite quantum state
International Nuclear Information System (INIS)
Cao Haijing; Chen Zhonghua; Song Heshan
2008-01-01
A controlled teleportation scheme of an unknown 3-dimensional (3D) two-particle quantum state is proposed, where a 3D Bell state and 3D GHZ state function as the quantum channel. This teleportation scheme can be directly generalized to teleport an unknown d-dimensional bipartite quantum state
Quantum phases of dipolar rotors on two-dimensional lattices.
Abolins, B P; Zillich, R E; Whaley, K B
2018-03-14
The quantum phase transitions of dipoles confined to the vertices of two-dimensional lattices of square and triangular geometry is studied using path integral ground state quantum Monte Carlo. We analyze the phase diagram as a function of the strength of both the dipolar interaction and a transverse electric field. The study reveals the existence of a class of orientational phases of quantum dipolar rotors whose properties are determined by the ratios between the strength of the anisotropic dipole-dipole interaction, the strength of the applied transverse field, and the rotational constant. For the triangular lattice, the generic orientationally disordered phase found at zero and weak values of both dipolar interaction strength and applied field is found to show a transition to a phase characterized by net polarization in the lattice plane as the strength of the dipole-dipole interaction is increased, independent of the strength of the applied transverse field, in addition to the expected transition to a transverse polarized phase as the electric field strength increases. The square lattice is also found to exhibit a transition from a disordered phase to an ordered phase as the dipole-dipole interaction strength is increased, as well as the expected transition to a transverse polarized phase as the electric field strength increases. In contrast to the situation with a triangular lattice, on square lattices, the ordered phase at high dipole-dipole interaction strength possesses a striped ordering. The properties of these quantum dipolar rotor phases are dominated by the anisotropy of the interaction and provide useful models for developing quantum phases beyond the well-known paradigms of spin Hamiltonian models, implementing in particular a novel physical realization of a quantum rotor-like Hamiltonian that possesses an anisotropic long range interaction.
Quantum phases of dipolar rotors on two-dimensional lattices
Abolins, B. P.; Zillich, R. E.; Whaley, K. B.
2018-03-01
The quantum phase transitions of dipoles confined to the vertices of two-dimensional lattices of square and triangular geometry is studied using path integral ground state quantum Monte Carlo. We analyze the phase diagram as a function of the strength of both the dipolar interaction and a transverse electric field. The study reveals the existence of a class of orientational phases of quantum dipolar rotors whose properties are determined by the ratios between the strength of the anisotropic dipole-dipole interaction, the strength of the applied transverse field, and the rotational constant. For the triangular lattice, the generic orientationally disordered phase found at zero and weak values of both dipolar interaction strength and applied field is found to show a transition to a phase characterized by net polarization in the lattice plane as the strength of the dipole-dipole interaction is increased, independent of the strength of the applied transverse field, in addition to the expected transition to a transverse polarized phase as the electric field strength increases. The square lattice is also found to exhibit a transition from a disordered phase to an ordered phase as the dipole-dipole interaction strength is increased, as well as the expected transition to a transverse polarized phase as the electric field strength increases. In contrast to the situation with a triangular lattice, on square lattices, the ordered phase at high dipole-dipole interaction strength possesses a striped ordering. The properties of these quantum dipolar rotor phases are dominated by the anisotropy of the interaction and provide useful models for developing quantum phases beyond the well-known paradigms of spin Hamiltonian models, implementing in particular a novel physical realization of a quantum rotor-like Hamiltonian that possesses an anisotropic long range interaction.
Topological Quantum Phase Transitions in Two-Dimensional Hexagonal Lattice Bilayers
Zhai, Xuechao; Jin, Guojun
2013-09-01
Since the successful fabrication of graphene, two-dimensional hexagonal lattice structures have become a research hotspot in condensed matter physics. In this short review, we theoretically focus on discussing the possible realization of a topological insulator (TI) phase in systems of graphene bilayer (GBL) and boron nitride bilayer (BNBL), whose band structures can be experimentally modulated by an interlayer bias voltage. Under the bias, a band gap can be opened in AB-stacked GBL but is still closed in AA-stacked GBL and significantly reduced in AA- or AB-stacked BNBL. In the presence of spin-orbit couplings (SOCs), further demonstrations indicate whether the topological quantum phase transition can be realized strongly depends on the stacking orders and symmetries of structures. It is observed that a bulk band gap can be first closed and then reopened when the Rashba SOC increases for gated AB-stacked GBL or when the intrinsic SOC increases for gated AA-stacked BNBL. This gives a distinct signal for a topological quantum phase transition, which is further characterized by a jump of the ℤ2 topological invariant. At fixed SOCs, the TI phase can be well switched by the interlayer bias and the phase boundaries are precisely determined. For AA-stacked GBL and AB-stacked BNBL, no strong TI phase exists, regardless of the strength of the intrinsic or Rashba SOCs. At last, a brief overview is given on other two-dimensional hexagonal materials including silicene and molybdenum disulfide bilayers.
Terahertz Plasma Waves in Two Dimensional Quantum Electron Gas with Electron Scattering
International Nuclear Information System (INIS)
Zhang Liping
2015-01-01
We investigate the Terahertz (THz) plasma waves in a two-dimensional (2D) electron gas in a nanometer field effect transistor (FET) with quantum effects, the electron scattering, the thermal motion of electrons and electron exchange-correlation. We find that, while the electron scattering, the wave number along y direction and the electron exchange-correlation suppress the radiation power, but the thermal motion of electrons and the quantum effects can amplify the radiation power. The radiation frequency decreases with electron exchange-correlation contributions, but increases with quantum effects, the wave number along y direction and thermal motion of electrons. It is worth mentioning that the electron scattering has scarce influence on the radiation frequency. These properties could be of great help to the realization of practical THz plasma oscillations in nanometer FET. (paper)
The propagator of quantum gravity in minisuperspace
International Nuclear Information System (INIS)
Louko, J.
1985-04-01
We study the quantum gravitational propagation amplitude between two spacelike three-surfaces in minisuperspaces where the supermomentum constraints are identically satisfied. We derive a well-defined path integral formula for the propagator and show that the propagator is an inverse of the canonical Hamiltonian operator. In an exactly solvable deSitter minisuperspace model the propagator is found to obey semi-classically correct boundary conditions. We discuss the implications for the full theory and suggest an approach to unravelling the physical meaning of the propagator. (orig.)
Correcting quantum errors with entanglement.
Brun, Todd; Devetak, Igor; Hsieh, Min-Hsiu
2006-10-20
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error-correcting codes, thus allowing us to "quantize" all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). For systems without large amounts of shared entanglement, these codes can also be used as catalytic codes, in which a small amount of initial entanglement enables quantum communication.
High-dimensional quantum cloning and applications to quantum hacking.
Bouchard, Frédéric; Fickler, Robert; Boyd, Robert W; Karimi, Ebrahim
2017-02-01
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.
Experiments on melting in classical and quantum two dimensional electron systems
International Nuclear Information System (INIS)
Williams, F.I.B.
1991-01-01
''Two dimensional electron system'' (2DES) here refers to electrons whose dynamics is free in 2 dimensions but blocked in the third. Experiments have been performed in two limiting situations: the classical, low density, limit realised by electrons deposited on a liquid helium surface and the quantum, high density, limit realised by electrons at an interface between two epitaxially matched semiconductors. In the classical system, where T Q c so that the thermodynamic state is determined by the competition between the temperature and the Coulomb interaction, melting is induced either by raising the temperature at constant density or by lowering the density at finite temperature. In the quantum system, it is not possible to lower the density below about 100n W without the Coulomb interaction losing out to the random field representing the extrinsic disorder imposed by the semiconductor host. Instead one has to induce crystallisation with the help of the Lorentz force, by applying a perpendicular magnetic field B [2] . As the quantum magnetic length l c = (Planck constant c/eB) 1/2 is reduced with respect to the interelectronic spacing a, expressed by the filling factor ν 2l c 2 /a 2 , the system exhibits the quantum Hall effect (QHE), first for integer then for fractional values of ν. The fractional quantum Hall effect (FQHE) is a result of Coulomb induced correlation in the quantum liquid, but as ν is decreased still further the correlations are expected to take on long-range crystal-like periodicity accompanied by elastic shear rigidity. Such a state can nonetheless be destroyed by the disordering effect of temperature, giving rise to a phase boundary in a (T, B) plane. The aim of experiment is first to determine the phase diagram and then to help elucidate the mechanism of the melting. (author)
Some exact results for the two-point function of an integrable quantum field theory
International Nuclear Information System (INIS)
Creamer, D.B.; Thacker, H.B.; Wilkinson, D.
1981-01-01
The two-point correlation function for the quantum nonlinear Schroedinger (one-dimensional delta-function gas) model is studied. An infinite-series representation for this function is derived using the quantum inverse-scattering formalism. For the case of zero temperature, the infinite-coupling (c→infinity) result of Jimbo, Miwa, Mori, and Sato is extended to give an exact expression for the order-1/c correction to the two-point function in terms of a Painleve transcendent of the fifth kind
Two-Dimensional One-Component Plasma on Flamm's Paraboloid
Fantoni, Riccardo; Téllez, Gabriel
2008-11-01
We study the classical non-relativistic two-dimensional one-component plasma at Coulomb coupling Γ=2 on the Riemannian surface known as Flamm's paraboloid which is obtained from the spatial part of the Schwarzschild metric. At this special value of the coupling constant, the statistical mechanics of the system are exactly solvable analytically. The Helmholtz free energy asymptotic expansion for the large system has been found. The density of the plasma, in the thermodynamic limit, has been carefully studied in various situations.
Quantum Information Processing and Quantum Error Correction An Engineering Approach
Djordjevic, Ivan
2012-01-01
Quantum Information Processing and Quantum Error Correction is a self-contained, tutorial-based introduction to quantum information, quantum computation, and quantum error-correction. Assuming no knowledge of quantum mechanics and written at an intuitive level suitable for the engineer, the book gives all the essential principles needed to design and implement quantum electronic and photonic circuits. Numerous examples from a wide area of application are given to show how the principles can be implemented in practice. This book is ideal for the electronics, photonics and computer engineer
Three-dimensional loop quantum gravity: towards a self-gravitating quantum field theory
International Nuclear Information System (INIS)
Noui, Karim
2007-01-01
In a companion paper, we have emphasized the role of the Drinfeld double DSU(2) in the context of three-dimensional Riemannian loop quantum gravity coupled to massive spinless point particles. We make use of this result to propose a model for a self-gravitating quantum field theory (massive spinless non-causal scalar field) in three-dimensional Riemannian space. We start by constructing the Fock space of the free self-gravitating field: the vacuum is the unique DSU(2) invariant state, one-particle states correspond to DSU(2) unitary irreducible simple representations and any multi-particles states are obtained as the symmetrized tensor product between simple representations. The associated quantum field is defined by the usual requirement of covariance under DSU(2). Then, we introduce a DSU(2)-invariant self-interacting potential (the obtained model is a group field theory) and explicitly compute the lowest order terms (in the self-interaction coupling constant λ) of the propagator and of the three-point function. Finally, we compute the lowest order quantum gravity corrections (in the Newton constant G) to the propagator and to the three-point function
Application of quasiexactly solvable potential method to the N-body ...
Indian Academy of Sciences (India)
physics pp. 985–996. Application of quasiexactly solvable potential method to the N-body ... Application of QES method to N-particle quantum model interacting via an ... Now, if we choose the centre of mass R as the origin of the coordinates,.
Two- to three-dimensional crossover in a dense electron liquid in silicon
Matmon, Guy; Ginossar, Eran; Villis, Byron J.; Kölker, Alex; Lim, Tingbin; Solanki, Hari; Schofield, Steven R.; Curson, Neil J.; Li, Juerong; Murdin, Ben N.; Fisher, Andrew J.; Aeppli, Gabriel
2018-04-01
Doping of silicon via phosphine exposures alternating with molecular beam epitaxy overgrowth is a path to Si:P substrates for conventional microelectronics and quantum information technologies. The technique also provides a well-controlled material for systematic studies of two-dimensional lattices with a half-filled band. We show here that for a dense (ns=2.8 ×1014 cm-2) disordered two-dimensional array of P atoms, the full field magnitude and angle-dependent magnetotransport is remarkably well described by classic weak localization theory with no corrections due to interaction. The two- to three-dimensional crossover seen upon warming can also be interpreted using scaling concepts developed for anistropic three-dimensional materials, which work remarkably except when the applied fields are nearly parallel to the conducting planes.
Quantum corrections to holographic mutual information
Energy Technology Data Exchange (ETDEWEB)
Agón, Cesar A. [Martin Fisher School of Physics, Brandeis University,Waltham, MA 02453 (United States); Faulkner, Thomas [University of Illinois, Urbana-Champaign,Urbana, IL 61801-3080 (United States)
2016-08-22
We compute the leading contribution to the mutual information (MI) of two disjoint spheres in the large distance regime for arbitrary conformal field theories (CFT) in any dimension. This is achieved by refining the operator product expansion method introduced by Cardy http://dx.doi.org/10.1088/1751-8113/46/28/285402. For CFTs with holographic duals the leading contribution to the MI at long distances comes from bulk quantum corrections to the Ryu-Takayanagi area formula. According to the FLM proposal http://dx.doi.org/10.1007/JHEP11(2013)074 this equals the bulk MI between the two disjoint regions spanned by the boundary spheres and their corresponding minimal area surfaces. We compute this quantum correction and provide in this way a non-trivial check of the FLM proposal.
Quantum corrections to holographic mutual information
International Nuclear Information System (INIS)
Agón, Cesar A.; Faulkner, Thomas
2016-01-01
We compute the leading contribution to the mutual information (MI) of two disjoint spheres in the large distance regime for arbitrary conformal field theories (CFT) in any dimension. This is achieved by refining the operator product expansion method introduced by Cardy http://dx.doi.org/10.1088/1751-8113/46/28/285402. For CFTs with holographic duals the leading contribution to the MI at long distances comes from bulk quantum corrections to the Ryu-Takayanagi area formula. According to the FLM proposal http://dx.doi.org/10.1007/JHEP11(2013)074 this equals the bulk MI between the two disjoint regions spanned by the boundary spheres and their corresponding minimal area surfaces. We compute this quantum correction and provide in this way a non-trivial check of the FLM proposal.
Analytically solvable models of reaction-diffusion systems
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)
2004-05-01
We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.
The background-quantum split symmetry in two-dimensional σ-models
International Nuclear Information System (INIS)
Blasi, A.; Delduc, F.; Sorella, S.P.
1989-01-01
A generic, non-linear, background-quantum split is translated into a BRS symmetry. The renormalization of the resulting Slavnov-Taylor identity is analyzed in the class of two-dimensional σ-models with Wess-Zumino term which suggests the adoption of a regularization independent method. We discuss the cohomology of the linearized nilpotent operator derived from the Slavnov-Taylor identity. In particular, the cohomology class with zero Faddeev-Popov charge ensures the stability of the action, while the fact that the cohomology class with one unit of Faddeev-Popov charge is empty ensures the absence of anomalies. (orig.)
BRST gauge fixing and regularization
International Nuclear Information System (INIS)
Damgaard, P.H.; Jonghe, F. de; Sollacher, R.
1995-05-01
In the presence of consistent regulators, the standard procedure of BRST gauge fixing (or moving from one gauge to another) can require non-trivial modifications. These modifications occur at the quantum level, and gauges exist which are only well-defined when quantum mechanical modifications are correctly taken into account. We illustrate how this phenomenon manifests itself in the solvable case of two-dimensional bosonization in the path-integral formalism. As a by-product, we show how to derive smooth bosonization in Batalin-Vilkovisky Lagrangian BRST quantization. (orig.)
An investigation of some quantum systems using modified quantization rule form
Energy Technology Data Exchange (ETDEWEB)
Maiz, F., E-mail: fethimaiz@gmail.com [University of Cartage, Nabeul Engineering Preparatory Institute, Merazka, 8000 Nabeul (Tunisia); King Khalid University, Faculty of Science, Physics Department, P.O. Box 9004, Abha 61413 (Saudi Arabia)
2014-09-15
We propose a new simple quantization rule form: J{sub n}=nπ+δ(n), for exactly solvable and nonsolvable quantum systems. Here, J{sub n} is the momentum integral between two turning points, n the principal quantum number, and δ(n) is a function of potential parameters and n. This new quantization rule form is a generalization of the conventional one, already developed for exactly solvable quantum systems. We found that δ(n) is a constant independent of n for exactly solvable quantum systems. We carry out the expression of δ(n) for V-shape potential, and show that it takes this form δ(n)=(π/2)+(1/a+bn+cn{sup 2}) for anharmonic oscillators potential V(x)=αx{sup p}+βx{sup 2}.
Quantum entanglement and phase transition in a two-dimensional photon-photon pair model
International Nuclear Information System (INIS)
Zhang Jianjun; Yuan Jianhui; Zhang Junpei; Cheng Ze
2013-01-01
We propose a two-dimensional model consisting of photons and photon pairs. In the model, the mixed gas of photons and photon pairs is formally equivalent to a two-dimensional system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phases. Using the variational method, we discuss the quantum phase transition of the mixed gas and obtain the critical coupling line analytically. Moreover, we also find that the phase transition of the photon gas can be interpreted as enhanced second harmonic generation. We then discuss the entanglement between photons and photon pairs. Additionally, we also illustrate how the entanglement between photons and photon pairs can be associated with the phase transition of the system.
Xu, Cenke
Several examples of quantum spin systems and pseudo spin systems have been studied, and unconventional states of matters and phase transitions have been realized in all these systems under consideration. In the p +/- ip superconductor Josephson lattice and the p--band cold atomic system trapped in optical lattices, novel phases which behave similarly to 1+1 dimensional systems are realized, despite the fact that the real physical systems are in two or three dimensional spaces. For instance, by employing a spin-wave analysis together with a new duality transformation, we establish the existence and stability of a novel gapless "critical phase", which we refer to as a "bond algebraic liquid". This novel critical phase is analogous to the 1+1 dimensional algebraic boson liquid phase. The reason for the novel physics is that there is a quasilocal gauge symmetry in the effective low energy Hamiltonian. In a spin-1 system on the kagome lattice, and a hard-core boson system on the honeycomb lattice, the low energy physics is controlled by two components of compact U(1) gauge symmetries that emerge at low energy. Making use of the confinement nature of the 2+1 dimensional compact gauge theories and the powerful duality between gauge theories and height field theories, the crystalline phase diagrams are studied for both systems, and the transitions to other phases are also considered. These phase diagrams might be accessible in strongly correlated materials, or atomic systems in optical lattices. A novel quantum ground state of matter is realized in a bosonic model on three dimensional fcc lattice with emergent low energy excitations. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the
Two dimensional spatial distortion correction algorithm for scintillation GAMMA cameras
International Nuclear Information System (INIS)
Chaney, R.; Gray, E.; Jih, F.; King, S.E.; Lim, C.B.
1985-01-01
Spatial distortion in an Anger gamma camera originates fundamentally from the discrete nature of scintillation light sampling with an array of PMT's. Historically digital distortion correction started with the method based on the distortion measurement by using 1-D slit pattern and the subsequent on-line bi-linear approximation with 64 x 64 look-up tables for X and Y. However, the X, Y distortions are inherently two-dimensional in nature, and thus the validity of this 1-D calibration method becomes questionable with the increasing distortion amplitude in association with the effort to get better spatial and energy resolutions. The authors have developed a new accurate 2-D correction algorithm. This method involves the steps of; data collection from 2-D orthogonal hole pattern, 2-D distortion vector measurement, 2-D Lagrangian polynomial interpolation, and transformation to X, Y ADC frame. The impact of numerical precision used in correction and the accuracy of bilinear approximation with varying look-up table size have been carefully examined through computer simulation by using measured single PMT light response function together with Anger positioning logic. Also the accuracy level of different order Lagrangian polynomial interpolations for correction table expansion from hole centroids were investigated. Detailed algorithm and computer simulation are presented along with camera test results
Quantum of optical absorption in two-dimensional semiconductors.
Fang, Hui; Bechtel, Hans A; Plis, Elena; Martin, Michael C; Krishna, Sanjay; Yablonovitch, Eli; Javey, Ali
2013-07-16
The optical absorption properties of free-standing InAs nanomembranes of thicknesses ranging from 3 nm to 19 nm are investigated by Fourier transform infrared spectroscopy. Stepwise absorption at room temperature is observed, arising from the interband transitions between the subbands of 2D InAs nanomembranes. Interestingly, the absorptance associated with each step is measured to be ∼1.6%, independent of thickness of the membranes. The experimental results are consistent with the theoretically predicted absorptance quantum, AQ = πα/nc for each set of interband transitions in a 2D semiconductor, where α is the fine structure constant and nc is an optical local field correction factor. Absorptance quantization appears to be universal in 2D systems including III-V quantum wells and graphene.
Dissipative quantum error correction and application to quantum sensing with trapped ions.
Reiter, F; Sørensen, A S; Zoller, P; Muschik, C A
2017-11-28
Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of noise. To protect them, the use of quantum error-correcting codes has been proposed. Trapped ions are an excellent technological platform for both quantum sensing and quantum error correction. Here we present a quantum error correction scheme that harnesses dissipation to stabilize a trapped-ion qubit. In our approach, always-on couplings to an engineered environment protect the qubit against spin-flips or phase-flips. Our dissipative error correction scheme operates in a continuous manner without the need to perform measurements or feedback operations. We show that the resulting enhanced coherence time translates into a significantly enhanced precision for quantum measurements. Our work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.
Czech Academy of Sciences Publication Activity Database
Šremr, Jiří
2007-01-01
Roč. 132, č. 3 (2007), s. 263-295 ISSN 0862-7959 R&D Projects: GA ČR GP201/04/P183 Institutional research plan: CEZ:AV0Z10190503 Keywords : system of functional differential equations with monotone operators * initial value problem * unique solvability Subject RIV: BA - General Mathematics
One dimensional models of excitons in carbon nanotubes
DEFF Research Database (Denmark)
Cornean, Horia Decebal; Duclos, P.; Pedersen, Thomas Garm
Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable.......Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable....
One-dimensional models of excitons in carbon nanotubes
DEFF Research Database (Denmark)
Cornean, Horia Decebal; Duclos, Pierre; Pedersen, Thomas Garm
2004-01-01
Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one-dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable.......Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one-dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable....
Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice
International Nuclear Information System (INIS)
Kim, Isaac H.
2011-01-01
We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.
Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice
Kim, Isaac H.
2011-05-01
We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.
Supersymmetry and quantum mechanics
International Nuclear Information System (INIS)
Cooper, F.; Sukhatme, U.
1995-01-01
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Approximation methods are also discussed within the framework of supersymmetric quantum mechanics and in particular it is shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate in a double well potential and for improving large N expansions. We also discuss the problem of a charged Dirac particle in an external magnetic field and other potentials in terms of supersymmetric quantum mechanics. Finally, we discuss structures more general than supersymmetric quantum mechanics such as parasupersymmetric quantum mechanics in which there is a symmetry between a boson and a para-fermion of order p. ((orig.))
Integrable finite-dimensional systems related to Lie algebras
International Nuclear Information System (INIS)
Olshanetsky, M.A.; Perelomov, A.M.
1979-01-01
Some solvable finite-dimensional classical and quantum systems related to the Lie algebras are considered. The dynamics of these systems is closely related to free motion on symmetric spaces. In specific cases the systems considered describe the one-dimensional n-body problem recently considered by many authors. The review represents from general and universal point of view the results obtained during the last few years. Besides, it contains some results both of physical and mathematical type
International Nuclear Information System (INIS)
Levanony, Dana; Ori, Amos
2010-01-01
We study the internal structure of a two-dimensional dilatonic evaporating black hole based on the Callan, Giddings, Harvey, and Strominger model. At the semiclassical level, a (weak) spacelike singularity was previously found to develop inside the black hole. We employ here a simplified quantum formulation of spacetime dynamics in the neighborhood of this singularity, using a minisuperspace-like approach. Quantum evolution is found to be regular and well defined at the semiclassical singularity. A well-localized initial wave packet propagating towards the singularity bounces off the latter and retains its well-localized form. Our simplified quantum treatment thus suggests that spacetime may extend semiclassically beyond the singularity, and also signifies the specific extension.
Levanony, Dana; Ori, Amos
2010-05-01
We study the internal structure of a two-dimensional dilatonic evaporating black hole based on the Callan, Giddings, Harvey, and Strominger model. At the semiclassical level, a (weak) spacelike singularity was previously found to develop inside the black hole. We employ here a simplified quantum formulation of spacetime dynamics in the neighborhood of this singularity, using a minisuperspace-like approach. Quantum evolution is found to be regular and well defined at the semiclassical singularity. A well-localized initial wave packet propagating towards the singularity bounces off the latter and retains its well-localized form. Our simplified quantum treatment thus suggests that spacetime may extend semiclassically beyond the singularity, and also signifies the specific extension.
Quantum corrections to Schwarzschild black hole
Energy Technology Data Exchange (ETDEWEB)
Calmet, Xavier; El-Menoufi, Basem Kamal [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)
2017-04-15
Using effective field theory techniques, we compute quantum corrections to spherically symmetric solutions of Einstein's gravity and focus in particular on the Schwarzschild black hole. Quantum modifications are covariantly encoded in a non-local effective action. We work to quadratic order in curvatures simultaneously taking local and non-local corrections into account. Looking for solutions perturbatively close to that of classical general relativity, we find that an eternal Schwarzschild black hole remains a solution and receives no quantum corrections up to this order in the curvature expansion. In contrast, the field of a massive star receives corrections which are fully determined by the effective field theory. (orig.)
Exactly solvable string models of curved space-time backgrounds
International Nuclear Information System (INIS)
Russo, J.G.
1995-01-01
We consider a new 3-parameter class of exact 4-dimensional solutions in closed string theory and solve the corresponding string model, determining the physical spectrum and the partition function. The background fields (4-metric, antisymmetric tensor, two Kaluza-Klein vector fields, dilaton and modulus) generically describe axially symmetric stationary rotating (electro)magnetic flux-tube type universes. Backgrounds of this class include both the ''dilatonic'' (a=1) and ''Kaluza-Klein'' (a=√(3)) Melvin solutions and the uniform magnetic field solution, as well as some singular space-times. Solvability of the string σ-model is related to its connection via duality to a simpler model which is a ''twisted'' product of a flat 2-space and a space dual to 2-plane. We discuss some physical properties of this model (tachyonic instabilities in the spectrum, gyromagnetic ratio, issue of singularities, etc.). It provides one of the first examples of a consistent solvable conformal string model with explicit D=4 curved space-time interpretation. (orig.)
Quantum state correction of relic gravitons from quantum gravity
Rosales, Jose-Luis
1996-01-01
The semiclassical approach to quantum gravity would yield the Schroedinger formalism for the wave function of metric perturbations or gravitons plus quantum gravity correcting terms in pure gravity; thus, in the inflationary scenario, we should expect correcting effects to the relic graviton (Zel'dovich) spectrum of the order (H/mPl)^2.
International Nuclear Information System (INIS)
Silagadze, Z.K.
2007-01-01
Two-dimensional generalization of the original peak finding algorithm suggested earlier is given. The ideology of the algorithm emerged from the well-known quantum mechanical tunneling property which enables small bodies to penetrate through narrow potential barriers. We merge this 'quantum' ideology with the philosophy of Particle Swarm Optimization to get the global optimization algorithm which can be called Quantum Swarm Optimization. The functionality of the newborn algorithm is tested on some benchmark optimization problems
Continuous-variable quantum erasure correcting code
DEFF Research Database (Denmark)
Lassen, Mikael Østergaard; Sabuncu, Metin; Huck, Alexander
2010-01-01
We experimentally demonstrate a continuous variable quantum erasure-correcting code, which protects coherent states of light against complete erasure. The scheme encodes two coherent states into a bi-party entangled state, and the resulting 4-mode code is conveyed through 4 independent channels...
Quantum confinement effect of two-dimensional all-inorganic halide perovskites
Cai, Bo; Li, Xiaoming; Gu, Yu; Harb, Moussab; Li, Jianhai; Xie, Meiqiu; Cao, Fei; Song, Jizhong; Zhang, Shengli; Cavallo, Luigi; Zeng, Haibo
2017-01-01
Quantum confinement effect (QCE), an essential physical phenomenon of semiconductors when the size becomes comparable to the exciton Bohr radius, typically results in quite different physical properties of low-dimensional materials from their bulk counterparts and can be exploited to enhance the device performance in various optoelectronic applications. Here, taking CsPbBr3 as an example, we reported QCE in all-inorganic halide perovskite in two-dimensional (2D) nanoplates. Blue shifts in optical absorption and photoluminescence spectra were found to be stronger in thinner nanoplates than that in thicker nanoplates, whose thickness lowered below ∼7 nm. The exciton binding energy results showed similar trend as that obtained for the optical absorption and photoluminescence. Meanwile, the function of integrated intensity and full width at half maximum and temperature also showed similar results, further supporting our conclusions. The results displayed the QCE in all-inorganic halide perovskite nanoplates and helped to design the all-inorganic halide perovskites with desired optical properties.
Quantum confinement effect of two-dimensional all-inorganic halide perovskites
Cai, Bo
2017-09-07
Quantum confinement effect (QCE), an essential physical phenomenon of semiconductors when the size becomes comparable to the exciton Bohr radius, typically results in quite different physical properties of low-dimensional materials from their bulk counterparts and can be exploited to enhance the device performance in various optoelectronic applications. Here, taking CsPbBr3 as an example, we reported QCE in all-inorganic halide perovskite in two-dimensional (2D) nanoplates. Blue shifts in optical absorption and photoluminescence spectra were found to be stronger in thinner nanoplates than that in thicker nanoplates, whose thickness lowered below ∼7 nm. The exciton binding energy results showed similar trend as that obtained for the optical absorption and photoluminescence. Meanwile, the function of integrated intensity and full width at half maximum and temperature also showed similar results, further supporting our conclusions. The results displayed the QCE in all-inorganic halide perovskite nanoplates and helped to design the all-inorganic halide perovskites with desired optical properties.
Two-dimensional macroscopic quantum tunneling in multi-gap superconductor Josephson junctions
International Nuclear Information System (INIS)
Asai, Hidehiro; Kawabata, Shiro; Ota, Yukihiro; Machida, Masahiko
2014-01-01
Low-temperature characters of superconducting devices yield definite probes for different superconducting phenomena. We study the macroscopic quantum tunneling (MQT) in a Josephson junction, composed of a single-gap superconductor and a two-gap superconductor. Since this junction has two kinds to the superconducting phase differences, calculating the MQT escape rate requires the analysis of quantum tunneling in a multi-dimensional configuration space. Our approach is the semi-classical approximation along a 1D curve in a 2D potential- energy landscape, connecting two adjacent potential (local) minimums through a saddle point. We find that this system has two plausible tunneling paths; an in-phase path and an out-of-phase path. The former is characterized by the Josephson-plasma frequency, whereas the latter is by the frequency of the characteristic collective mode in a two-band superconductor, Josephson- Leggett mode. Depending on external bias current and inter-band Josephson-coupling energy, one of them mainly contributes to the MQT. Our numerical calculations show that the difference between the in-phase path and the out-of-phase path is manifest, with respect to the bias- current-dependence of the MQT escape rate. This result suggests that our MQT setting be an indicator of the Josephson-Leggett mode
Directory of Open Access Journals (Sweden)
W.Janke
2006-01-01
Full Text Available This paper gives a brief introduction to using two-dimensional discrete and Euclidean quantum gravity approaches as a laboratory for studying the properties of fluctuating and frozen random graphs in interaction with "matter fields" represented by simple spin or vertex models. Due to the existence of numerous exact analytical results and predictions for comparison with simulational work, this is an interesting and useful enterprise.
High-Dimensional Single-Photon Quantum Gates: Concepts and Experiments.
Babazadeh, Amin; Erhard, Manuel; Wang, Feiran; Malik, Mehul; Nouroozi, Rahman; Krenn, Mario; Zeilinger, Anton
2017-11-03
Transformations on quantum states form a basic building block of every quantum information system. From photonic polarization to two-level atoms, complete sets of quantum gates for a variety of qubit systems are well known. For multilevel quantum systems beyond qubits, the situation is more challenging. The orbital angular momentum modes of photons comprise one such high-dimensional system for which generation and measurement techniques are well studied. However, arbitrary transformations for such quantum states are not known. Here we experimentally demonstrate a four-dimensional generalization of the Pauli X gate and all of its integer powers on single photons carrying orbital angular momentum. Together with the well-known Z gate, this forms the first complete set of high-dimensional quantum gates implemented experimentally. The concept of the X gate is based on independent access to quantum states with different parities and can thus be generalized to other photonic degrees of freedom and potentially also to other quantum systems.
International Nuclear Information System (INIS)
Xu Wen; Guo Yong
2005-01-01
We investigate the influence of the Rashba and Dresselhaus spin-orbit coupling interactions on tunnelling through two-dimensional magnetic quantum systems. It is showed that not only Rashba spin-orbit coupling but also Dresselhaus one can affect spin tunnelling properties greatly in such a quantum system. The transmission possibility, the spin polarization and the conductance are obviously oscillated with both coupling strengths. High spin polarization, conductance and magnetic conductance of the structure can be obtained by modulating either Rashba or Dresselhaus coupling strength
Nonadiabatic corrections to a quantum dot quantum computer
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 83; Issue 1. Nonadiabatic corrections to a quantum dot quantum computer working in adiabatic limit. M Ávila ... The time of operation of an adiabatic quantum computer must be less than the decoherence time, otherwise the computer would be nonoperative. So far, the ...
International Nuclear Information System (INIS)
Tokuhisa, Atsushi; Taka, Junichiro; Kono, Hidetoshi; Go, Nobuhiro
2012-01-01
A new algorithm is developed for reconstructing the high-resolution three-dimensional diffraction intensity function of a globular biological macromolecule from many quantum-noise-limited two-dimensional X-ray laser diffraction patterns, each for an unknown orientation. The structural resolution is expressed as a function of the incident X-ray intensity and quantities characterizing the target molecule. A new two-step algorithm is developed for reconstructing the three-dimensional diffraction intensity of a globular biological macromolecule from many experimentally measured quantum-noise-limited two-dimensional X-ray laser diffraction patterns, each for an unknown orientation. The first step is classification of the two-dimensional patterns into groups according to the similarity of direction of the incident X-rays with respect to the molecule and an averaging within each group to reduce the noise. The second step is detection of common intersecting circles between the signal-enhanced two-dimensional patterns to identify their mutual location in the three-dimensional wavenumber space. The newly developed algorithm enables one to detect a signal for classification in noisy experimental photon-count data with as low as ∼0.1 photons per effective pixel. The wavenumber of such a limiting pixel determines the attainable structural resolution. From this fact, the resolution limit due to the quantum noise attainable by this new method of analysis as well as two important experimental parameters, the number of two-dimensional patterns to be measured (the load for the detector) and the number of pairs of two-dimensional patterns to be analysed (the load for the computer), are derived as a function of the incident X-ray intensity and quantities characterizing the target molecule
Integrability and solvability of the simplified two-qubit Rabi model
International Nuclear Information System (INIS)
Peng Jie; Ren Zhongzhou; Guo Guangjie; Ju Guoxing
2012-01-01
The simplified two-qubit Rabi model is proposed and its analytical solution is presented. There are no level crossings in the spectral graph of the model, which indicates that it is not integrable. The criterion of integrability for the Rabi model proposed by Braak (2011 Phys. Rev. Lett. 107 100401) is also used for the simplified two-qubit Rabi model and the same conclusion, consistent with what the spectral graph shows, can be drawn, which indicates that the criterion remains valid when applied to the two-qubit case. The simplified two-qubit Rabi model is another example of a non-integrable but exactly solvable system except for the generalized Rabi model. (paper)
Quantum mechanics and hidden superconformal symmetry
Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.
2017-12-01
Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp (1 |2 ) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp (1 |2 ) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models—both oscillator and particlelike—realize all possible unitary irreducible representations of osp (1 |2 ).
Quantum integrable models of field theory
International Nuclear Information System (INIS)
Faddeev, L.D.
1979-01-01
Fundamental features of the classical method of the inverse problem have been formulated in the form which is convenient for its quantum reformulation. Typical examples are studied which may help to formulate the quantum method of the inverse problem. Examples are considered for interaction with both attraction and repulsion at a final density. The sine-Gordon model and the XYZ model from the quantum theory of magnetics are examined in short. It is noted that all the achievements of the one-dimensional mathematical physics as applied to exactly solvable quantum models may be put to an extent within the framework of the quantum method of the inverse problem. Unsolved questions are enumerated and perspectives of applying the inverse problem method are shown
Temperature dependent transport of two dimensional electrons in the integral quantum Hall regime
International Nuclear Information System (INIS)
Wi, H.P.
1986-01-01
This thesis is concerned with the temperature dependent electronic transport properties of a two dimensional electron gas subject to background potential fluctuations and a perpendicular magnetic field. The author carried out an extensive temperature dependent study of the transport coefficients, in the region of an integral quantum plateau, in an In/sub x/Ga/sub 1-x/As/InP heterostructure for 4.2K 10 cm -2 meV -1 ) even at the middle between two Landau levels, which is unexpected from model calculations based on short ranged randomness. In addition, the different T dependent behavior of rho/sub xx/ between the states in the tails and those near the center of a Landau level, indicates the existence of different electron states in a Landau level. Additionally, the author reports T-dependent transport measurements in the transition region between two quantum plateaus in several different materials
Energy Technology Data Exchange (ETDEWEB)
Weber, Carsten
2008-07-01
This work is focused on the optical dynamics of mesoscopic semiconductor heterostructures, using as prototypes zero-dimensional quantum dots and quantum cascade lasers which consist of quasitwo- dimensional quantum wells. Within a density matrix theory, a microscopic many-particle theory is applied to study scattering effects in these structures: the coupling to external as well as local fields, electron-phonon coupling, coupling to impurities, and Coulomb coupling. For both systems, the investigated effects are compared to experimentally observed results obtained during the past years. In quantum dots, the three-dimensional spatial confinement leads to the necessity to consider a quantum kinetic description of the dynamics, resulting in non-Markovian electron-phonon effects. This can be seen in the spectral phonon sidebands due to interaction with acoustic phonons as well as a damping of nonlinear Rabi oscillations which shows a nonmonotonous intensity and pulse duration dependence. An analysis of the inclusion of the self-interaction of the quantum dot shows that no dynamical local field terms appear for the simple two-level model. Considering local fields which have their origin in many quantum dots, consequences for a two-level quantum dot such as a zero-phonon line broadening and an increasing signal in photon echo experiments are found. For the use of quantum dots in an optical spin control scheme, it is found that the dephasing due to the electron-phonon interaction can be dominant in certain regimes. Furthermore, soliton and breather solutions are studied analytically in nonlinear quantum dot ensembles. Generalizing to quasi-two-dimensional structures, the intersubband dynamics of quantum cascade laser structures is investigated. A dynamical theory is considered in which the temporal evolution of the subband populations and the current density as well as the influence of scattering effects is studied. In the nonlinear regime, the scattering dependence and
Two new types of solvability of the one-dimensional anharmonic oscillators
International Nuclear Information System (INIS)
Znojil, M.
1989-01-01
In the Schroedinger picture, we propose a new modification of the so-called Hill-determinant technique. It is shown to guarantee a proper matching of the two underlying power series Ψ(x) at x=0. In the Heisenberg picture, an evolution of the same one-dimensional polynomially anharmonic oscillator is considered. A modified Peano-Baker method is applied and shown to define the explicit solutions by recurrences. 11 refs
Entanglement renormalization, quantum error correction, and bulk causality
Energy Technology Data Exchange (ETDEWEB)
Kim, Isaac H. [IBM T.J. Watson Research Center,1101 Kitchawan Rd., Yorktown Heights, NY (United States); Kastoryano, Michael J. [NBIA, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen (Denmark)
2017-04-07
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated by a local Hamiltonian.
Quantum Corrections to the 'Atomistic' MOSFET Simulations
Asenov, Asen; Slavcheva, G.; Kaya, S.; Balasubramaniam, R.
2000-01-01
We have introduced in a simple and efficient manner quantum mechanical corrections in our 3D 'atomistic' MOSFET simulator using the density gradient formalism. We have studied in comparison with classical simulations the effect of the quantum mechanical corrections on the simulation of random dopant induced threshold voltage fluctuations, the effect of the single charge trapping on interface states and the effect of the oxide thickness fluctuations in decanano MOSFETs with ultrathin gate oxides. The introduction of quantum corrections enhances the threshold voltage fluctuations but does not affect significantly the amplitude of the random telegraph noise associated with single carrier trapping. The importance of the quantum corrections for proper simulation of oxide thickness fluctuation effects has also been demonstrated.
Quantum Fidelity and Thermal Phase Transitions in a Two-Dimensional Spin System
International Nuclear Information System (INIS)
Wang Bo; Kou Su-Peng; Huang Hai-Lin; Sun Zhao-Yu
2012-01-01
We investigate the ability of quantum fidelity in detecting the classical phase transitions (CPTs) in a two-dimensional Heisenberg—Ising mixed spin model, which has a very rich phase diagram and is exactly soluble. For a two-site subsystem of the model, the reduced fidelity (including the operator fidelity and the fidelity susceptibility) at finite temperatures is calculated, and it is found that an extreme value presents at the critical temperature, thus shows a signal for the CPTs. In some parameter region, the signal becomes blurred. We propose to use the 'normalized fidelity susceptibility' to solve this problem
Optimal conclusive teleportation of a d-dimensional two-particle unknown quantum state
Institute of Scientific and Technical Information of China (English)
Yang Yu-Guang; Wen Qiao-Yan; Zhu Fu-Chen
2006-01-01
A conclusive teleportation protocol of a d-dimensional two-particle unknown quantum state using three ddimensional particles in an arbitrary pure state is proposed. A sender teleports the unknown state conclusively to a receiver by using the positive operator valued measure(POVM) and introducing an ancillary qudit to perform the generalized Bell basis measurement. We calculate the optimal teleportation fidelity. We also discuss and analyse the reason why the information on the teleported state is lost in the course of the protocol.
Leading quantum correction to the Newtonian potential
International Nuclear Information System (INIS)
Donoghue, J.F.
1994-01-01
I argue that the leading quantum corrections, in powers of the energy or inverse powers of the distance, may be computed in quantum gravity through knowledge of only the low-energy structure of the theory. As an example, I calculate the leading quantum corrections to the Newtonian gravitational potential
International Nuclear Information System (INIS)
Bouchard, A.M.
1994-01-01
This report discusses the following topics: Bloch oscillations and other dynamical phenomena of electrons in semiconductor superlattices; solvable dynamical model of an electron in a one-dimensional aperiodic lattice subject to a uniform electric field; and quantum dynamical phenomena of electrons in aperiodic semiconductor superlattices
Eight exactly solvable comples potentials in Bender - Boettcher quantum mechanics
Czech Academy of Sciences Publication Activity Database
Znojil, Miloslav
2001-01-01
Roč. 2, č. 66 (2001), s. 213-218 ISSN 0009-725X. [The 20th Winter Schooll "Geometry and Physics". Srní, 15.01.2000-22.01.2000] R&D Projects: GA AV ČR IAA1048004 Keywords : solvable * potentials * bound-state Subject RIV: BE - Theoretical Physics
Topology Change and the Emergence of Geometry in Two Dimensional Causal Quantum Gravity
Westra, W.
2007-01-01
Despite many attempts, gravity has vigorously resisted a unification with the laws of quantum mechanics. Besides a plethora of technical issues, one is also faced with many interesting conceptual problems. The study of quantum gravity in lower dimensional models ameliorates the technical
Quantum corrections to inflaton and curvaton dynamics
Energy Technology Data Exchange (ETDEWEB)
Markkanen, Tommi [Helsinki Institute of Physics and Department of Physics, University of Helsinki, P.O. Box 64, FI-00014, Helsinki (Finland); Tranberg, Anders, E-mail: tommi.markkanen@helsinki.fi, E-mail: anders.tranberg@nbi.dk [Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen (Denmark)
2012-11-01
We compute the fully renormalized one-loop effective action for two interacting and self-interacting scalar fields in FRW space-time. We then derive and solve the quantum corrected equations of motion both for fields that dominate the energy density (such as an inflaton) and fields that do not (such as a subdominant curvaton). In particular, we introduce quantum corrected Friedmann equations that determine the evolution of the scale factor. We find that in general, gravitational corrections are negligible for the field dynamics. For the curvaton-type fields this leaves only the effect of the flat-space Coleman-Weinberg-type effective potential, and we find that these can be significant. For the inflaton case, both the corrections to the potential and the Friedmann equations can lead to behaviour very different from the classical evolution. Even to the point that inflation, although present at tree level, can be absent at one-loop order.
International Nuclear Information System (INIS)
Contreras-Astorga, A.; Negro, J.; Tristao, S.
2016-01-01
This paper deals with the problem of an electron in a non-homogeneous magnetic field perpendicular to a plane. From the classical point of view this is an integrable, but not superintegrable, solvable system. In the quantum framework of the Dirac equation this integrable system is solvable too; the energy levels and wavefunctions of bound states, for its reduction to the plane, are computed. The effective one-dimensional matrix Hamiltonian is shown to belong to a shape-invariant hierarchy. Through this example we will shed some light on the specific properties of a quantum integrable system with respect to those characteristic of superintegrable systems. - Highlights: • The system: an electron in a non-homogeneous magnetic field. • This is a solvable integrable but not superintegrable system. • Solutions to the discrete Dirac spectrum are found. • The shape-invariance of Dirac matrix Hamiltonians is characterized. • Specific properties of integrable, not superintegrable, systems are analyzed.
Energy Technology Data Exchange (ETDEWEB)
Contreras-Astorga, A., E-mail: alonso.contreras.astorga@gmail.com [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, IN 46408 (United States); Departamento de Física, Cinvestav, A.P. 14-740, 07000 México D.F. (Mexico); Negro, J., E-mail: jnegro@fta.uva.es [Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, E-47011 Valladolid (Spain); Tristao, S., E-mail: hetsudoyaguiu@gmail.com [Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, E-47011 Valladolid (Spain)
2016-01-08
This paper deals with the problem of an electron in a non-homogeneous magnetic field perpendicular to a plane. From the classical point of view this is an integrable, but not superintegrable, solvable system. In the quantum framework of the Dirac equation this integrable system is solvable too; the energy levels and wavefunctions of bound states, for its reduction to the plane, are computed. The effective one-dimensional matrix Hamiltonian is shown to belong to a shape-invariant hierarchy. Through this example we will shed some light on the specific properties of a quantum integrable system with respect to those characteristic of superintegrable systems. - Highlights: • The system: an electron in a non-homogeneous magnetic field. • This is a solvable integrable but not superintegrable system. • Solutions to the discrete Dirac spectrum are found. • The shape-invariance of Dirac matrix Hamiltonians is characterized. • Specific properties of integrable, not superintegrable, systems are analyzed.
Energy Technology Data Exchange (ETDEWEB)
Pokhabov, D. A., E-mail: pokhabov@isp.nsc.ru; Pogosov, A. G.; Budantsev, M. V.; Zhdanov, E. Yu.; Bakarov, A. K. [Russian Academy of Sciences, Rzhanov Institute of Semiconductor Physics, Siberian Branch (Russian Federation)
2016-08-15
The nonequilibrium state of a two-dimensional electron gas in the quantum-Hall-effect regime is studied in Hall bars equipped with additional inner contacts situated within the bar. The magnetic-field dependence of the voltage drop between different contact pairs are studied at various temperatures. It was found that the voltage between the inner and outer contacts exhibits peaks of significant amplitude in narrow magnetic-field intervals near integer filling factors. Furthermore, the magnetic-field dependence of the voltage in these intervals exhibits a hysteresis, whereas the voltage between the outer contacts remains zero in the entire magnetic-field range. The appearance of the observed voltage peaks and their hysteretic behavior can be explained by an imbalance between the chemical potentials of edge and bulk states, resulting from nonequilibrium charge redistribution between the edge and bulk states when the magnetic field sweeps under conditions of the quantum Hall effect. The results of the study significantly complement the conventional picture of the quantum Hall effect, explicitly indicating the existence of a significant imbalance at the edge of the two-dimensional electron gas: the experimentally observed difference between the electrochemical potentials of the edge and bulk exceeds the distance between Landau levels by tens of times.
Quantum Dots in Two-Dimensional Perovskite Matrices for Efficient Near-Infrared Light Emission
Yang, Zhenyu
2017-03-13
Quantum-dot-in-perovskite solids are excellent candidates for infrared light-emitting applications. The first generation of dot-in-perovskite light-emitting diodes (LEDs) has shown bright infrared electroluminescence with tunable emission wavelength; however, their performance has been limited by degradation of the active layer at practical operating voltages. This arises from the instability of the three-dimensional (3D) organolead halide perovskite matrix. Herein we report the first dot-in-perovskite solids that employ two-dimensional (2D) perovskites as the matrix. 2D perovskite passivation is achieved via an in situ alkylammonium/alkylamine substitution carried out during the quantum dot (QD) ligand exchange process. This single-step film preparation process enables deposition of the QD/perovskite active layers with thicknesses of 40 nm, over seven times thinner than the first-generation dot-in-perovskite thin films that relied on a multistep synthesis. The dot-in-perovskite film roughness improved from 31 nm for the first-generation films to 3 nm for films as a result of this new approach. The best devices exhibit external quantum efficiency peaks exceeding 2% and radiances of ∼1 W sr–1 m–2, with an improved breakdown voltage up to 7.5 V. Compared to first-generation dot-in-perovskites, this new process reduces materials consumptions 10-fold and represents a promising step toward manufacturable devices.
Quantum Dots in Two-Dimensional Perovskite Matrices for Efficient Near-Infrared Light Emission
Yang, Zhenyu; Voznyy, Oleksandr; Walters, Grant; Fan, James Z.; Liu, Min; Kinge, Sachin; Hoogland, Sjoerd; Sargent, Edward H.
2017-01-01
Quantum-dot-in-perovskite solids are excellent candidates for infrared light-emitting applications. The first generation of dot-in-perovskite light-emitting diodes (LEDs) has shown bright infrared electroluminescence with tunable emission wavelength; however, their performance has been limited by degradation of the active layer at practical operating voltages. This arises from the instability of the three-dimensional (3D) organolead halide perovskite matrix. Herein we report the first dot-in-perovskite solids that employ two-dimensional (2D) perovskites as the matrix. 2D perovskite passivation is achieved via an in situ alkylammonium/alkylamine substitution carried out during the quantum dot (QD) ligand exchange process. This single-step film preparation process enables deposition of the QD/perovskite active layers with thicknesses of 40 nm, over seven times thinner than the first-generation dot-in-perovskite thin films that relied on a multistep synthesis. The dot-in-perovskite film roughness improved from 31 nm for the first-generation films to 3 nm for films as a result of this new approach. The best devices exhibit external quantum efficiency peaks exceeding 2% and radiances of ∼1 W sr–1 m–2, with an improved breakdown voltage up to 7.5 V. Compared to first-generation dot-in-perovskites, this new process reduces materials consumptions 10-fold and represents a promising step toward manufacturable devices.
International Nuclear Information System (INIS)
Dakaloyannis, C.
2006-01-01
Full text: (author)The two dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar as the classical ones multiplied by a quantum coefficient -n 2 plus a quantum deformation of order n 4 and n 6 . The systems inside the classes are transformed using Stackel transforms in the quantum case as in the classical case and general form is discussed. The idea of the Jacobi Hamiltonian corresponding to the Jacobi metric in the classical case is discussed
In-plane g factor of low-density two-dimensional holes in a Ge quantum well.
Energy Technology Data Exchange (ETDEWEB)
Lu, Tzu-Ming [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Harris, Charles Thomas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Huang, Shih-Hsien [National Taiwan Univ., Taipei (Taiwan); Chuang, Yen [National Taiwan Univ., Taipei (Taiwan); Li, Jiun-Yun [National Taiwan Univ., Taipei (Taiwan); Liu, CheeWee [National Taiwan Univ., Taipei (Taiwan)
2017-12-01
High-mobility two-dimensional (2D) holes residing in a Ge quantum well are a new electronic system with potentials in quantum computing and spintronics. Since for any electronic material, the effective mass and the g factor are two fundamental material parameters that determine the material response to electric and magnetic fields, measuring these two parameters in this material system is thus an important task that needs to be completed urgently. Because of the quantum confinement in the crystal growth direction (z), the biaxial strain of epitaxial Ge on SiGe, and the valance band nature, both the effective mass and the g factor can show very strong anisotropy. In particular, the in-plane g factor (g_{ip}) can be vanishingly small while the perpendicular g factor (g_{z}) can be much larger than 2. Here we report the measurement of g_{ip} at very low hole densities using in-plane magneto-resistance measurement performed at the NHMFL.
Energy Technology Data Exchange (ETDEWEB)
Choi, Hyunwoo, E-mail: chw0089@gmail.com [Department of Electrical and Computer Engineering, University of Seoul, Seoul 02504 (Korea, Republic of); Kim, Tae Geun, E-mail: tgkim1@korea.ac.kr [School of Electrical Engineering, Korea University, Seoul 02841 (Korea, Republic of); Shin, Changhwan, E-mail: cshin@uos.ac.kr [Department of Electrical and Computer Engineering, University of Seoul, Seoul 02504 (Korea, Republic of)
2017-06-15
Highlights: • The quantum capacitance in topological insulator (TI) at room temperature is directly revealed. • The physical origin of quantum capacitance, the two dimensional surface state of TI, is experimentally validated. • Theoretically calculated results of ideal quantum capacitance can well predict the experimental data. - Abstract: A topological insulator (TI) is a new kind of material that exhibits unique electronic properties owing to its topological surface state (TSS). Previous studies focused on the transport properties of the TSS, since it can be used as the active channel layer in metal-oxide-semiconductor field-effect transistors (MOSFETs). However, a TI with a negative quantum capacitance (QC) effect can be used in the gate stack of MOSFETs, thereby facilitating the creation of ultra-low power electronics. Therefore, it is important to study the physics behind the QC in TIs in the absence of any external magnetic field, at room temperature. We fabricated a simple capacitor structure using a TI (TI-capacitor: Au-TI-SiO{sub 2}-Si), which shows clear evidence of QC at room temperature. In the capacitance-voltage (C-V) measurement, the total capacitance of the TI-capacitor increases in the accumulation regime, since QC is the dominant capacitive component in the series capacitor model (i.e., C{sub T}{sup −1} = C{sub Q}{sup −1} + C{sub SiO2}{sup −1}). Based on the QC model of the two-dimensional electron systems, we quantitatively calculated the QC, and observed that the simulated C-V curve theoretically supports the conclusion that the QC of the TI-capacitor is originated from electron–electron interaction in the two-dimensional surface state of the TI.
International Nuclear Information System (INIS)
Sedrakian, D.M.; Badalyan, D.H.; Sedrakian, L.R.
2015-01-01
Quasi-one-dimensional quantum particle scattering on two-dimensional δ-potential is considered. Analytical expressions for the amplitudes of the multi-channel transmission and reflection are given. The problem for the case when the number of channels is finite and equal N, and the particle falls on the potential moving through the channel l is solved. The case of a three channel scattering is studied in details. It is shown that under conditions k 2 → 0 and k 3 → 0 'overpopulation' of particles on the second and third channels occurs. The points of δ-potential location which provide a full 'overpopulation' of particles is also found
Two-dimensional gauge model with vector U(1) and axial-vector U(1) symmetries
International Nuclear Information System (INIS)
Watabiki, Y.
1989-01-01
We have succeeded in constructing a two-dimensional gauge model with both vector U(1) and axial-vector U(1) symmetries. This model is exactly solvable. The Schwinger term vanishes in this model as a consequence of the above symmetries, and negative-norm states appear. However, the norms of physical states are always positive semidefinite due to the gauge symmetries
Quantum key distribution session with 16-dimensional photonic states
Etcheverry, S.; Cañas, G.; Gómez, E. S.; Nogueira, W. A. T.; Saavedra, C.; Xavier, G. B.; Lima, G.
2013-01-01
The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD. PMID:23897033
Low-energy effective action in two-dimensional SQED: a two-loop analysis
Samsonov, I. B.
2017-07-01
We study two-loop quantum corrections to the low-energy effective actions in N=(2,2) and N=(4,4) SQED on the Coulomb branch. In the latter model, the low-energy effective action is described by a generalized Kähler potential which depends on both chiral and twisted chiral superfields. We demonstrate that this generalized Kähler potential is one-loop exact and corresponds to the N=(4,4) sigma-model with torsion presented by Roček, Schoutens and Sevrin [1]. In the N=(2,2) SQED, the effective Kähler potential is not protected against higher-loop quantum corrections. The two-loop quantum corrections to this potential and the corresponding sigma-model metric are explicitly found.
Integrable models of quantum optics
Directory of Open Access Journals (Sweden)
Yudson Vladimir
2017-01-01
Full Text Available We give an overview of exactly solvable many-body models of quantum optics. Among them is a system of two-level atoms which interact with photons propagating in a one-dimensional (1D chiral waveguide; exact eigenstates of this system can be explicitly constructed. This approach is used also for a system of closely located atoms in the usual (non-chiral waveguide or in 3D space. Moreover, it is shown that for an arbitrary atomic system with a cascade spontaneous radiative decay, the fluorescence spectrum can be described by an exact analytic expression which accounts for interference of emitted photons. Open questions related with broken integrability are discussed.
Shen, H Z; Shao, X Q; Wang, G C; Zhao, X L; Yi, X X
2016-01-01
The quantum phase transition (QPT) describes a sudden qualitative change of the macroscopic properties mapped from the eigenspectrum of a quantum many-body system. It has been studied intensively in quantum systems with the spin-boson model, but it has barely been explored for systems in coupled spin-boson models. In this paper, we study the QPT with coupled spin-boson models consisting of coupled two-level atoms embedded in three-dimensional anisotropic photonic crystals. The dynamics of the system is derived exactly by means of the Laplace transform method, which has been proven to be equivalent to the dissipationless non-Markovian dynamics. Drawing on methods for analyzing the ground state, we obtain the phase diagrams through two exact critical equations and two QPTs are found: one QPT is that from the phase without one bound state to the phase with one bound state and another is that from one phase with the bound state having one eigenvalue to another phase where the bound state has two eigenvalues. Our analytical results also suggest a way of control to overcome the effect of decoherence by engineering the spectrum of the reservoirs to approach the non-Markovian regime and to form the bound state of the whole system for quantum devices and quantum statistics.
Effect of FLR correction on Rayleigh -Taylor instability of quantum and stratified plasma
International Nuclear Information System (INIS)
Sharma, P.K.; Tiwari, Anita; Argal, Shraddha; Chhajlani, R.K.
2013-01-01
The Rayleigh Taylor instability of stratified incompressible fluids is studied in presence of FLR Correction and quantum effects in bounded medium. The Quantum magneto hydrodynamic equations of the problem are solved by using normal mode analysis method. A dispersion relation is carried out for the case where plasma is bounded by two rigid planes z = 0 and z = h. The dispersion relation is obtained in dimensionless form to discuss the growth rate of Rayleigh Taylor instability in presence of FLR Correction and quantum effects. The stabilizing or destabilizing behavior of quantum effect and FLR correction on the Rayleigh Taylor instability is analyzed. (author)
Stochastic quantum gravity-(2+1)-dimensional case
International Nuclear Information System (INIS)
Hosoya, Akio
1991-01-01
At first the amazing coincidences are pointed out in quantum field theory in curved space-time and quantum gravity, when they exhibit stochasticity. To explore the origin of them, the (2+1)-dimensional quantum gravity is considered as a toy model. It is shown that the torus universe in the (2+1)-dimensional quantum gravity is a quantum chaos in a rigorous sense. (author). 15 refs
Bound on quantum computation time: Quantum error correction in a critical environment
International Nuclear Information System (INIS)
Novais, E.; Mucciolo, Eduardo R.; Baranger, Harold U.
2010-01-01
We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user.
Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators
Niu, Murphy Yuezhen; Chuang, Isaac L.; Shapiro, Jeffrey H.
2018-03-01
We establish a symmetry-operator framework for designing quantum error-correcting (QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes that are suitable for χ(2 )-interaction based quantum computation in multimode Fock bases: the χ(2 ) parity-check code, the χ(2 ) embedded error-correcting code, and the χ(2 ) binomial code. All of these QEC codes detect photon-loss or photon-gain errors by means of photon-number parity measurements, and then correct them via χ(2 ) Hamiltonian evolutions and linear-optics transformations. Our symmetry-operator framework provides a systematic procedure for finding QEC codes that are not stabilizer codes, and it enables convenient extension of a given encoding to higher-dimensional qudit bases. The χ(2 ) binomial code is of special interest because, with m ≤N identified from channel monitoring, it can correct m -photon-loss errors, or m -photon-gain errors, or (m -1 )th -order dephasing errors using logical qudits that are encoded in O (N ) photons. In comparison, other bosonic QEC codes require O (N2) photons to correct the same degree of bosonic errors. Such improved photon efficiency underscores the additional error-correction power that can be provided by channel monitoring. We develop quantum Hamming bounds for photon-loss errors in the code subspaces associated with the χ(2 ) parity-check code and the χ(2 ) embedded error-correcting code, and we prove that these codes saturate their respective bounds. Our χ(2 ) QEC codes exhibit hardware efficiency in that they address the principal error mechanisms and exploit the available physical interactions of the underlying hardware, thus reducing the physical resources required for implementing their encoding, decoding, and error-correction operations, and their universal encoded-basis gate sets.
Experimental quantum annealing: case study involving the graph isomorphism problem.
Zick, Kenneth M; Shehab, Omar; French, Matthew
2015-06-08
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N(2) to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers.
Achieving the Heisenberg limit in quantum metrology using quantum error correction.
Zhou, Sisi; Zhang, Mengzhen; Preskill, John; Jiang, Liang
2018-01-08
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.
Loop quantum corrected Einstein Yang-Mills black holes
Protter, Mason; DeBenedictis, Andrew
2018-05-01
In this paper, we study the homogeneous interiors of black holes possessing SU(2) Yang-Mills fields subject to corrections inspired by loop quantum gravity. The systems studied possess both magnetic and induced electric Yang-Mills fields. We consider the system of equations both with and without Wilson loop corrections to the Yang-Mills potential. The structure of the Yang-Mills Hamiltonian, along with the restriction to homogeneity, allows for an anomaly-free effective quantization. In particular, we study the bounce which replaces the classical singularity and the behavior of the Yang-Mills fields in the quantum corrected interior, which possesses topology R ×S2 . Beyond the bounce, the magnitude of the Yang-Mills electric field asymptotically grows monotonically. This results in an ever-expanding R sector even though the two-sphere volume is asymptotically constant. The results are similar with and without Wilson loop corrections on the Yang-Mills potential.
Two-dimensional topological field theories coupled to four-dimensional BF theory
International Nuclear Information System (INIS)
Montesinos, Merced; Perez, Alejandro
2008-01-01
Four-dimensional BF theory admits a natural coupling to extended sources supported on two-dimensional surfaces or string world sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two-dimensional world sheet. We show how two-dimensional Yang-Mills degrees of freedom can be added on the world sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two-dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background-independent quantum field theory where local degrees of freedom at low energies arise from global topological (world sheet) degrees of freedom at the fundamental level
Quantum corrections for spinning particles in de Sitter
Energy Technology Data Exchange (ETDEWEB)
Fröb, Markus B. [Department of Mathematics, University of York, Heslington, York, YO10 5DD (United Kingdom); Verdaguer, Enric, E-mail: mbf503@york.ac.uk, E-mail: enric.verdaguer@ub.edu [Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos (ICC), Universitat de Barcelona (UB), C/ Martí i Franquès 1, 08028 Barcelona (Spain)
2017-04-01
We compute the one-loop quantum corrections to the gravitational potentials of a spinning point particle in a de Sitter background, due to the vacuum polarisation induced by conformal fields in an effective field theory approach. We consider arbitrary conformal field theories, assuming only that the theory contains a large number N of fields in order to separate their contribution from the one induced by virtual gravitons. The corrections are described in a gauge-invariant way, classifying the induced metric perturbations around the de Sitter background according to their behaviour under transformations on equal-time hypersurfaces. There are six gauge-invariant modes: two scalar Bardeen potentials, one transverse vector and one transverse traceless tensor, of which one scalar and the vector couple to the spinning particle. The quantum corrections consist of three different parts: a generalisation of the flat-space correction, which is only significant at distances of the order of the Planck length; a constant correction depending on the undetermined parameters of the renormalised effective action; and a term which grows logarithmically with the distance from the particle. This last term is the most interesting, and when resummed gives a modified power law, enhancing the gravitational force at large distances. As a check on the accuracy of our calculation, we recover the linearised Kerr-de Sitter metric in the classical limit and the flat-space quantum correction in the limit of vanishing Hubble constant.
Tokuhisa, Atsushi; Taka, Junichiro; Kono, Hidetoshi; Go, Nobuhiro
2012-05-01
A new two-step algorithm is developed for reconstructing the three-dimensional diffraction intensity of a globular biological macromolecule from many experimentally measured quantum-noise-limited two-dimensional X-ray laser diffraction patterns, each for an unknown orientation. The first step is classification of the two-dimensional patterns into groups according to the similarity of direction of the incident X-rays with respect to the molecule and an averaging within each group to reduce the noise. The second step is detection of common intersecting circles between the signal-enhanced two-dimensional patterns to identify their mutual location in the three-dimensional wavenumber space. The newly developed algorithm enables one to detect a signal for classification in noisy experimental photon-count data with as low as ~0.1 photons per effective pixel. The wavenumber of such a limiting pixel determines the attainable structural resolution. From this fact, the resolution limit due to the quantum noise attainable by this new method of analysis as well as two important experimental parameters, the number of two-dimensional patterns to be measured (the load for the detector) and the number of pairs of two-dimensional patterns to be analysed (the load for the computer), are derived as a function of the incident X-ray intensity and quantities characterizing the target molecule. © 2012 International Union of Crystallography
Quantum secret sharing based on quantum error-correcting codes
International Nuclear Information System (INIS)
Zhang Zu-Rong; Liu Wei-Tao; Li Cheng-Zu
2011-01-01
Quantum secret sharing(QSS) is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k − 1, 1, k] quantum error-correcting code (QECC) to implement a quantum (k, 2k − 1) threshold scheme. It also takes advantage of classical enhancement of the [2k − 1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels. (general)
Modeling A.C. Electronic Transport through a Two-Dimensional Quantum Point Contact
International Nuclear Information System (INIS)
Aronov, I.E.; Beletskii, N.N.; Berman, G.P.; Campbell, D.K.; Doolen, G.D.; Dudiy, S.V.
1998-01-01
We present the results on the a.c. transport of electrons moving through a two-dimensional (2D) semiconductor quantum point contact (QPC). We concentrate our attention on the characteristic properties of the high frequency admittance (ωapproximately0 - 50 GHz), and on the oscillations of the admittance in the vicinity of the separatrix (when a channel opens or closes), in presence of the relaxation effects. The experimental verification of such oscillations in the admittance would be a strong confirmation of the semi-classical approach to the a.c. transport in a QPC, in the separatrix region
Searching for quantum solitons in a (3+1)-dimensional chiral Yukawa model
International Nuclear Information System (INIS)
Farhi, E.; Graham, N.; Jaffe, R.L.; Weigel, H.
2002-01-01
We search for static solitons stabilized by heavy fermions in a (3+1)-dimensional Yukawa model. We compute the renormalized energy functional, including the exact one-loop quantum corrections, and perform a variational search for configurations that minimize the energy for a fixed fermion number. We compute the quantum corrections using a phase shift parameterization, in which we renormalize by identifying orders of the Born series with corresponding Feynman diagrams. For higher-order terms in the Born series, we develop a simplified calculational method. When applicable, we use the derivative expansion to check our results. We observe marginally bound configurations at large Yukawa coupling, and discuss their interpretation as soliton solutions subject to general limitations of the model
Fickler, Robert; Lapkiewicz, Radek; Huber, Marcus; Lavery, Martin P J; Padgett, Miles J; Zeilinger, Anton
2014-07-30
Photonics has become a mature field of quantum information science, where integrated optical circuits offer a way to scale the complexity of the set-up as well as the dimensionality of the quantum state. On photonic chips, paths are the natural way to encode information. To distribute those high-dimensional quantum states over large distances, transverse spatial modes, like orbital angular momentum possessing Laguerre Gauss modes, are favourable as flying information carriers. Here we demonstrate a quantum interface between these two vibrant photonic fields. We create three-dimensional path entanglement between two photons in a nonlinear crystal and use a mode sorter as the quantum interface to transfer the entanglement to the orbital angular momentum degree of freedom. Thus our results show a flexible way to create high-dimensional spatial mode entanglement. Moreover, they pave the way to implement broad complex quantum networks where high-dimensionally entangled states could be distributed over distant photonic chips.
Quantum walk with a four-dimensional coin
International Nuclear Information System (INIS)
Hamilton, Craig S; Gabris, Aurel; Jex, Igor; Barnett, Stephen M
2011-01-01
We examine the physical implementation of a discrete time quantum walk with a four-dimensional coin. Our quantum walker is a photon moving repeatedly through a time delay loop, with time being our position space. The quantum coin is implemented using the internal states of the photon: the polarization and two of the orbital angular momentum states. We demonstrate how to implement this physically and what components would be needed. We then illustrate some of the results that could be obtained by performing the experiment.
Topological order in an exactly solvable 3D spin model
International Nuclear Information System (INIS)
Bravyi, Sergey; Leemhuis, Bernhard; Terhal, Barbara M.
2011-01-01
Research highlights: RHtriangle We study exactly solvable spin model with six-qubit nearest neighbor interactions on a 3D face centered cubic lattice. RHtriangle The ground space of the model exhibits topological quantum order. RHtriangle Elementary excitations can be geometrically described as the corners of rectangular-shaped membranes. RHtriangle The ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. RHtriangle Logical operators acting on the encoded qubits are described in terms of closed strings and closed membranes. - Abstract: We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest-neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on Ω(R 2 ) qubits. Composite particles that consist of two monopoles (dipoles) and four monopoles (quadrupoles) can be described as end-points of strings. The peculiar feature of the model is that dipole-type strings are rigid, that is, such strings must be aligned with face-diagonals of the lattice. For periodic boundary conditions the ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. We describe a complete set of logical operators acting on the encoded qubits in terms of closed strings and closed membranes.
A model of the two-dimensional quantum harmonic oscillator in an AdS{sub 3} background
Energy Technology Data Exchange (ETDEWEB)
Frick, R. [Universitaet zu Koeln, Institut fuer Theoretische Physik, Cologne (Germany)
2016-10-15
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a three-dimensional anti-de Sitter background. We use a generalized Schroedinger picture in which the analogs of the Schroedinger operators of the particle are independent of both the time and the space coordinates in different representations. The spacetime independent operators of the particle induce the Lie algebra of Killing vector fields of the AdS{sub 3} spacetime. In this picture, we have a metamorphosis of the Heisenberg uncertainty relations. (orig.)
Nonadiabatic corrections to a quantum dot quantum computer ...
Indian Academy of Sciences (India)
2014-07-02
Jul 2, 2014 ... corrections in it. If the decoherence times of a quantum dot computer are ∼100 ns [J M Kikkawa and D D Awschalom, Phys. Rev. Lett. 80, 4313 (1998)] then the predicted number of one qubit gate (primitive) operations of the Loss–DiVincenzo quantum computer in such an interval of time must be >1010.
On the confinement of a Dirac particle to a two-dimensional ring
International Nuclear Information System (INIS)
Bakke, K.; Furtado, C.
2012-01-01
In this contribution, we propose a new model for studying the confinement of a spin-half particle to a two-dimensional quantum ring for systems described by the Dirac equation by introducing a new coupling into the Dirac equation. We show that the introduction of this new coupling into the Dirac equation yields a generalization of the two-dimensional quantum ring model proposed by Tan and Inkson [W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11 (1996) 1635] for relativistic spin-half quantum particles. -- Highlights: ► Two-dimensional ring model for condensed matter systems described by the Dirac equation. ► Exact solutions of the Dirac equation. ► Persistent currents for Dirac-like systems confined to a two-dimensional quantum ring.
International Nuclear Information System (INIS)
Schroer, Bert; Freie Universitaet, Berlin
2005-02-01
It is not possible to compactly review the overwhelming literature on two-dimensional models in a meaningful way without a specific viewpoint; I have therefore tacitly added to the above title the words 'as theoretical laboratories for general quantum field theory'. I dedicate this contribution to the memory of J. A. Swieca with whom I have shared the passion of exploring 2-dimensional models for almost one decade. A shortened version of this article is intended as a contribution to the project 'Encyclopedia of mathematical physics' and comments, suggestions and critical remarks are welcome. (author)
Wormholes in higher dimensions with non-linear curvature terms from quantum gravity corrections
Energy Technology Data Exchange (ETDEWEB)
El-Nabulsi, Ahmad Rami [Neijiang Normal University, Neijiang, Sichuan (China)
2011-11-15
In this work, we discuss a 7-dimensional universe in the presence of a static traversable wormhole and a decaying cosmological constant and dominated by higher-order curvature effects expected from quantum gravity corrections. We confirmed the existence of wormhole solutions in the form of the Lovelock gravity. Many interesting and attractive features are discussed in some detail.
Inhomogeneous Quantum Invariance Group of Multi-Dimensional Multi-parameter Deformed Boson Algebra
International Nuclear Information System (INIS)
Altintas Azmi Ali; Arik Metin; Arikan Ali Serdar; Dil Emre
2012-01-01
We investigate the inhomogeneous invariance quantum group of the d-dimensional d-parameter deformed boson algebra. It is found that the homogeneous part of this quantum group is given by the d-parameter deformed general linear group. We construct the R-matrix which collects all information about the non-commuting structure of the quantum group for the two-dimensional case. (general)
Autonomous Quantum Error Correction with Application to Quantum Metrology
Reiter, Florentin; Sorensen, Anders S.; Zoller, Peter; Muschik, Christine A.
2017-04-01
We present a quantum error correction scheme that stabilizes a qubit by coupling it to an engineered environment which protects it against spin- or phase flips. Our scheme uses always-on couplings that run continuously in time and operates in a fully autonomous fashion without the need to perform measurements or feedback operations on the system. The correction of errors takes place entirely at the microscopic level through a build-in feedback mechanism. Our dissipative error correction scheme can be implemented in a system of trapped ions and can be used for improving high precision sensing. We show that the enhanced coherence time that results from the coupling to the engineered environment translates into a significantly enhanced precision for measuring weak fields. In a broader context, this work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
Energy Technology Data Exchange (ETDEWEB)
Thapliyal, Kishore, E-mail: tkishore36@yahoo.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India); Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in [Indian Institute of Technology Jodhpur, Jodhpur 342011 (India); Pathak, Anirban, E-mail: anirban.pathak@gmail.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India)
2016-03-15
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
International Nuclear Information System (INIS)
Thapliyal, Kishore; Banerjee, Subhashish; Pathak, Anirban
2016-01-01
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.
Theory of ground state factorization in quantum cooperative systems.
Giampaolo, Salvatore M; Adesso, Gerardo; Illuminati, Fabrizio
2008-05-16
We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows us to determine rigorously the existence, location, and exact form of separable ground states in a large variety of, generally nonexactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary range.
Massive quantum field theory in two-dimensional Robertson-Walker space-time
International Nuclear Information System (INIS)
Bunch, T.S.; Christensen, S.M.; Fulling, S.A.
1978-01-01
The stress tensor of a massive scalar field, as an integral over normal modes (which are not mere plane waves), is regularized by covariant point separation. When the expectation value in a Parker-Fulling adiabatic vacuum state is expanded in the limit of small curvature-to-mass ratios, the series coincides in each order with the Schwinger-DeWitt-Christensen proper-time expansion. The renormalization ansatz suggested by these expansions (which applies to arbitrary curvature-to-mass ratios and arbitrary quantum state) can be implemented at the integrand level for practical computations. The renormalized tensor (1) passes in the massless limit, for appropriate choice of state, to the known vacuum stress of a massless field, (2) agrees with the explicit results of Bernard and Duncan for a special model, and (3) has a nonzero vacuum expectation value in the two-dimensional ''Milne universe'' (flat space in hyperbolic coordinates). Following Wald, we prove that the renormalized tensor is conserved and point out that there is no arbitrariness in the renormalization procedure. The general approach of this paper is applicable to four-dimensional models
Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Paul, J.; Dey, P.; Karaiskaj, D., E-mail: karaiskaj@usf.edu [Department of Physics, University of South Florida, 4202 East Fowler Ave., Tampa, Florida 33620 (United States); Tokumoto, T.; Hilton, D. J. [Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294 (United States); Reno, J. L. [CINT, Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)
2014-10-07
The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ∼4 × 10{sup 11} cm{sup −2} was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent “rephasing” (S{sub 1}) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S{sub 1} 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The “two-quantum coherence” (S{sub 3}) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.
Exactly solvable model of the two-dimensional electrical double layer.
Samaj, L; Bajnok, Z
2005-12-01
We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike unit charges in the stability-against-collapse regime of reduced inverse temperatures 0layer) carries some nonzero surface charge density. The model is mappable onto an integrable semi-infinite sine-Gordon theory with Dirichlet boundary conditions. The exact form-factor and boundary state information gained from the mapping provide asymptotic forms of the charge and number density profiles of electrolyte particles at large distances from the interface. The result for the asymptotic behavior of the induced electric potential, related to the charge density via the Poisson equation, confirms the validity of the concept of renormalized charge and the corresponding saturation hypothesis. It is documented on the nonperturbative result for the asymptotic density profile at a strictly nonzero beta that the Debye-Hückel beta-->0 limit is a delicate issue.
Quantum-corrected drift-diffusion models for transport in semiconductor devices
International Nuclear Information System (INIS)
De Falco, Carlo; Gatti, Emilio; Lacaita, Andrea L.; Sacco, Riccardo
2005-01-01
In this paper, we propose a unified framework for Quantum-corrected drift-diffusion (QCDD) models in nanoscale semiconductor device simulation. QCDD models are presented as a suitable generalization of the classical drift-diffusion (DD) system, each particular model being identified by the constitutive relation for the quantum-correction to the electric potential. We examine two special, and relevant, examples of QCDD models; the first one is the modified DD model named Schroedinger-Poisson-drift-diffusion, and the second one is the quantum-drift-diffusion (QDD) model. For the decoupled solution of the two models, we introduce a functional iteration technique that extends the classical Gummel algorithm widely used in the iterative solution of the DD system. We discuss the finite element discretization of the various differential subsystems, with special emphasis on their stability properties, and illustrate the performance of the proposed algorithms and models on the numerical simulation of nanoscale devices in two spatial dimensions
High-Dimensional Quantum Information Processing with Linear Optics
Fitzpatrick, Casey A.
Quantum information processing (QIP) is an interdisciplinary field concerned with the development of computers and information processing systems that utilize quantum mechanical properties of nature to carry out their function. QIP systems have become vastly more practical since the turn of the century. Today, QIP applications span imaging, cryptographic security, computation, and simulation (quantum systems that mimic other quantum systems). Many important strategies improve quantum versions of classical information system hardware, such as single photon detectors and quantum repeaters. Another more abstract strategy engineers high-dimensional quantum state spaces, so that each successful event carries more information than traditional two-level systems allow. Photonic states in particular bring the added advantages of weak environmental coupling and data transmission near the speed of light, allowing for simpler control and lower system design complexity. In this dissertation, numerous novel, scalable designs for practical high-dimensional linear-optical QIP systems are presented. First, a correlated photon imaging scheme using orbital angular momentum (OAM) states to detect rotational symmetries in objects using measurements, as well as building images out of those interactions is reported. Then, a statistical detection method using chains of OAM superpositions distributed according to the Fibonacci sequence is established and expanded upon. It is shown that the approach gives rise to schemes for sorting, detecting, and generating the recursively defined high-dimensional states on which some quantum cryptographic protocols depend. Finally, an ongoing study based on a generalization of the standard optical multiport for applications in quantum computation and simulation is reported upon. The architecture allows photons to reverse momentum inside the device. This in turn enables realistic implementation of controllable linear-optical scattering vertices for
Smooth controllability of infinite-dimensional quantum-mechanical systems
International Nuclear Information System (INIS)
Wu, Re-Bing; Tarn, Tzyh-Jong; Li, Chun-Wen
2006-01-01
Manipulation of infinite-dimensional quantum systems is important to controlling complex quantum dynamics with many practical physical and chemical backgrounds. In this paper, a general investigation is casted to the controllability problem of quantum systems evolving on infinite-dimensional manifolds. Recognizing that such problems are related with infinite-dimensional controllability algebras, we introduce an algebraic mathematical framework to describe quantum control systems possessing such controllability algebras. Then we present the concept of smooth controllability on infinite-dimensional manifolds, and draw the main result on approximate strong smooth controllability. This is a nontrivial extension of the existing controllability results based on the analysis over finite-dimensional vector spaces to analysis over infinite-dimensional manifolds. It also opens up many interesting problems for future studies
Universal corrections to entanglement entropy of local quantum quenches
Energy Technology Data Exchange (ETDEWEB)
David, Justin R.; Khetrapal, Surbhi [Centre for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore 560012 (India); Kumar, S. Prem [Department of Physics, Swansea University,Singleton Park, Swansea SA2 8PP (United Kingdom)
2016-08-22
We study the time evolution of single interval Rényi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width ϵ. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Rényi and entanglement entropies at order ϵ{sup 2} is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the ϵ{sup 2} correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential μ. We calculate the time dependence of the order ϵ{sup 2} correction to the entanglement entropy for small μ, and show that the contribution at order μ{sup 2} is universal. We verify our arguments against exact results for minimal models and the free fermion theory.
Higher order corrections in quantum electrodynamics
International Nuclear Information System (INIS)
Rafael, E.
1977-01-01
Theoretical contributions to high-order corrections in purely leptonic systems, such as electrons and muons, muonium (μ + e - ) and positronium (e + e - ), are reviewed to establish the validity of quantum electrodynamics (QED). Two types of QED contributions to the anomalous magnetic moments are considered, from diagrams with one fermion type lines and those witn two fermion type lines. The contributions up to eighth order are compared to the data available with a different accuracy. Good agreement is stated within the experimental errors. The experimental accuracy of the muonium hyperfine structure and of the radiative corrections to the decay of positronium are compared to the one attainable in theoretical calculations. The need for a higher precision in both experimental data and theoretical calculations is stated
Finite-dimensional effects and critical indices of one-dimensional quantum models
International Nuclear Information System (INIS)
Bogolyubov, N.M.; Izergin, A.G.; Reshetikhin, N.Yu.
1986-01-01
Critical indices, depending on continuous parameters in Bose-gas quantum models and Heisenberg 1/2 spin antiferromagnetic in two-dimensional space-time at zero temperature, have been calculated by means of finite-dimensional effects. In this case the long-wave asymptotics of the correlation functions is of a power character. Derivation of man asymptotics terms is reduced to the determination of a central charge in the appropriate Virassoro algebra representation and the anomalous dimension-operator spectrum in this representation. The finite-dimensional effects allow to find these values
Exactly solvable string models of curved space-time backgrounds
Russo, J.G.; Russo, J G; Tseytlin, A A
1995-01-01
We consider a new 3-parameter class of exact 4-dimensional solutions in closed string theory and solve the corresponding string model, determining the physical spectrum and the partition function. The background fields (4-metric, antisymmetric tensor, two Kaluza-Klein vector fields, dilaton and modulus) generically describe axially symmetric stationary rotating (electro)magnetic flux-tube type universes. Backgrounds of this class include both the dilatonic Melvin solution and the uniform magnetic field solution discussed earlier as well as some singular space-times. Solvability of the string sigma model is related to its connection via duality to a much simpler looking model which is a "twisted" product of a flat 2-space and a space dual to 2-plane. We discuss some physical properties of this model as well as a number of generalizations leading to larger classes of exact 4-dimensional string solutions.
Gravity, two times, tractors, Weyl invariance, and six-dimensional quantum mechanics
International Nuclear Information System (INIS)
Bonezzi, R.; Latini, E.; Waldron, A.
2010-01-01
Fefferman and Graham showed some time ago that four-dimensional conformal geometries could be analyzed in terms of six-dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently, it was shown how conformal geometry provides a description of physics manifestly invariant under local choices of unit systems. Strikingly, Einstein's equations are then equivalent to the existence of a parallel scale tractor (a six-component vector subject to a certain first order covariant constancy condition at every point in four-dimensional spacetime). These results suggest a six-dimensional description of four-dimensional physics, a viewpoint promulgated by the 2 times physics program of Bars. The Fefferman-Graham construction relies on a triplet of operators corresponding, respectively, to a curved six-dimensional light cone, the dilation generator and the Laplacian. These form an sp(2) algebra which Bars employs as a first class algebra of constraints in a six-dimensional gauge theory. In this article four-dimensional gravity is recast in terms of six-dimensional quantum mechanics by melding the 2 times and tractor approaches. This parent formulation of gravity is built from an infinite set of six-dimensional fields. Successively integrating out these fields yields various novel descriptions of gravity including a new four-dimensional one built from a scalar doublet, a tractor-vector multiplet and a conformal class of metrics.
Feasibility of self-correcting quantum memory and thermal stability of topological order
International Nuclear Information System (INIS)
Yoshida, Beni
2011-01-01
Recently, it has become apparent that the thermal stability of topologically ordered systems at finite temperature, as discussed in condensed matter physics, can be studied by addressing the feasibility of self-correcting quantum memory, as discussed in quantum information science. Here, with this correspondence in mind, we propose a model of quantum codes that may cover a large class of physically realizable quantum memory. The model is supported by a certain class of gapped spin Hamiltonians, called stabilizer Hamiltonians, with translation symmetries and a small number of ground states that does not grow with the system size. We show that the model does not work as self-correcting quantum memory due to a certain topological constraint on geometric shapes of its logical operators. This quantum coding theoretical result implies that systems covered or approximated by the model cannot have thermally stable topological order, meaning that systems cannot be stable against both thermal fluctuations and local perturbations simultaneously in two and three spatial dimensions. - Highlights: → We define a class of physically realizable quantum codes. → We determine their coding and physical properties completely. → We establish the connection between topological order and self-correcting memory. → We find they do not work as self-correcting quantum memory. → We find they do not have thermally stable topological order.
n-dimensional FLRW quantum cosmology
International Nuclear Information System (INIS)
Letelier, Patricio S.; Pitelli, Joao Paulo M.
2010-01-01
We introduce the formalism of quantum cosmology in a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe of arbitrary dimension filled with a perfect fluid with p=αρ equation of state. First we show that the Schutz formalism, developed in four dimensions, can be extended to a n-dimensional universe. We compute the quantum representant of the scale factor a(t), in the Many-Worlds, as well as, in the de Broglie-Bohm interpretation of quantum mechanics. We show that the singularities, which are still present in the n-dimensional generalization of FLRW universe, are excluded with the introduction of quantum theory. We quantize, via the de Broglie-Bohm interpretation of quantum mechanics, the components of the Riemann curvature tensor in a tetrad basis in a n-dimensional FLRW universe filled with radiation (p=(1/n-1)ρ). We show that the quantized version of the Ricci scalar are perfectly regular for all time t. We also study the behavior of the energy density and pressure and show that the ratio L / L tends to the classical value 1/(n-1) only for n=4, showing that n=4 is somewhat privileged among the other dimensions. Besides that, as n→∞, L / L →1.
Quantum trajectories in complex space: One-dimensional stationary scattering problems
International Nuclear Information System (INIS)
Chou, C.-C.; Wyatt, Robert E.
2008-01-01
One-dimensional time-independent scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. The equation for the local approximate quantum trajectories near the stagnation point of the quantum momentum function is derived, and the first derivative of the quantum momentum function is related to the local structure of quantum trajectories. Exact complex quantum trajectories are determined for two examples by numerically integrating the equations of motion. For the soft potential step, some particles penetrate into the nonclassical region, and then turn back to the reflection region. For the barrier scattering problem, quantum trajectories may spiral into the attractors or from the repellers in the barrier region. Although the classical potentials extended to complex space show different pole structures for each problem, the quantum potentials present the same second-order pole structure in the reflection region. This paper not only analyzes complex quantum trajectories and the total potentials for these examples but also demonstrates general properties and similar structures of the complex quantum trajectories and the quantum potentials for one-dimensional time-independent scattering problems
Malpetti, Daniele; Roscilde, Tommaso
2017-02-01
The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical
Tensor Networks and Quantum Error Correction
Ferris, Andrew J.; Poulin, David
2014-07-01
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.
Entanglement and Quantum Error Correction with Superconducting Qubits
Reed, Matthew
2015-03-01
Quantum information science seeks to take advantage of the properties of quantum mechanics to manipulate information in ways that are not otherwise possible. Quantum computation, for example, promises to solve certain problems in days that would take a conventional supercomputer the age of the universe to decipher. This power does not come without a cost however, as quantum bits are inherently more susceptible to errors than their classical counterparts. Fortunately, it is possible to redundantly encode information in several entangled qubits, making it robust to decoherence and control imprecision with quantum error correction. I studied one possible physical implementation for quantum computing, employing the ground and first excited quantum states of a superconducting electrical circuit as a quantum bit. These ``transmon'' qubits are dispersively coupled to a superconducting resonator used for readout, control, and qubit-qubit coupling in the cavity quantum electrodynamics (cQED) architecture. In this talk I will give an general introduction to quantum computation and the superconducting technology that seeks to achieve it before explaining some of the specific results reported in my thesis. One major component is that of the first realization of three-qubit quantum error correction in a solid state device, where we encode one logical quantum bit in three entangled physical qubits and detect and correct phase- or bit-flip errors using a three-qubit Toffoli gate. My thesis is available at arXiv:1311.6759.
Inflationary power spectra with quantum holonomy corrections
Energy Technology Data Exchange (ETDEWEB)
Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, Reymonta 4, Cracow, 30-059 Poland (Poland)
2014-03-01
In this paper we study slow-roll inflation with holonomy corrections from loop quantum cosmology. It was previously shown that, in the Planck epoch, these corrections lead to such effects as singularity avoidance, metric signature change and a state of silence. Here, we consider holonomy corrections affecting the phase of cosmic inflation, which takes place away from the Planck epoch. Both tensor and scalar power spectra of primordial inflationary perturbations are computed up to the first order in slow-roll parameters and V/ρ{sub c}, where V is a potential of the scalar field and ρ{sub c} is a critical energy density (expected to be of the order of the Planck energy density). Possible normalizations of modes at short scales are discussed. In case the normalization is performed with use of the Wronskian condition applied to adiabatic vacuum, the tensor and scalar spectral indices are not quantum corrected in the leading order. However, by choosing an alternative method of normalization one can obtain quantum corrections in the leading order. Furthermore, we show that the holonomy-corrected equations of motion for tensor and scalar modes can be derived based on effective background metrics. This allows us to show that the classical Wronskian normalization condition is well defined for the cosmological perturbations with holonomy corrections.
Quantum Secure Direct Communication by Using Three-Dimensional Hyperentanglement
International Nuclear Information System (INIS)
Shi Jin; Gong Yanxiao; Xu Ping; Zhu Shining; Zhan Youbang
2011-01-01
We propose two schemes for realizing quantum secure direct communication (QSDC) by using a set of ordered two-photon three-dimensional hyperentangled states entangled in two degrees of freedom (DOFs) as quantum information channels. In the first scheme, the photons from Bob to Alice are transmitted only once. After insuring the security of the quantum channels, Bob encodes the secret message on his photons. Then Alice performs single-photon two-DOF Bell bases measurements on her photons. This scheme has better security than former QSDC protocols. In the second scheme, Bob transmits photons to Alice twice. After insuring the security of the quantum channels, Bob encodes the secret message on his photons. Then Alice performs two-photon Bell bases measurements on each DOF. The scheme has more information capacity than former QSDC protocols. (general)
Supersymmetric quantum mechanics: another nontrivial quantum superpotential
International Nuclear Information System (INIS)
Cervero, J.M.
1991-01-01
A nontrivial example of a quantum superpotential in the framework of supersymmetric quantum mechanics is constructed using integrable soliton-like functions. The model is shown to be fully solvable and some consequences regarding the physical properties of the model such as transparence and boundary effects are discussed. (orig.)
Mean Field Analysis of Quantum Annealing Correction.
Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A
2016-06-03
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
Two-loop scale-invariant scalar potential and quantum effective operators
Ghilencea, D.M.
2016-11-29
Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a higgs-like scalar $\\phi$ in theories in which scale symmetry is broken only spontaneously by the dilaton ($\\sigma$). Its vev $\\langle\\sigma\\rangle$ generates the DR subtraction scale ($\\mu\\sim\\langle\\sigma\\rangle$), which avoids the explicit scale symmetry breaking by traditional regularizations (where $\\mu$=fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking ($\\mu$=fixed scale). These operators have the form: $\\phi^6/\\sigma^2$, $\\phi^8/\\sigma^4$, etc, which generate an infinite series of higher dimensional polynomial operators upon expansion about $\\langle\\sigma\\rangle\\gg \\langle\\phi\\rangle$, where such hierarchy is arranged by {\\it one} initial, classical tuning. These operators emerge at the quantum...
International Nuclear Information System (INIS)
Gruzintsev, A.N.; Volkov, V.T.; Emelchenko, G.A.; Karpov, I.A.; Maslov, W.M.; Michailov, G.M.; Yakimov, E.E.
2004-01-01
The luminescence properties of ZnO films of different thickness obtained on a synthetic opal were investigated. Several narrow peaks in the exciton emission region related to the size quantum effect of the electron wave functions were detected. Two-dimensional ordered array of ZnO quantum dots formed inside the opal pores on the second sphere layer were found by the atomic force microscopy (AFM) and angle dependence of the luminescence spectra
Quantum censorship in two dimensions
Energy Technology Data Exchange (ETDEWEB)
Pangon, V. [Frankfurt Institute for Advanced Studies, Universitaet Frankfurt, D-60438 Frankfurt am Main (Germany); Gesellschaft fuer Schwerionenforschung mbH, Planckstr. 1, D-64291 Darmstadt (Germany); Nagy, S. [Department of Theoretical Physics, University of Debrecen, Debrecen (Hungary); Polonyi, J., E-mail: polonyi@ires.in2p3.f [Strasbourg University, CNRS-IPHC, BP28 67037 Strasbourg Cedex 2 (France); Sailer, K. [Department of Theoretical Physics, University of Debrecen, Debrecen (Hungary)
2010-10-25
It is pointed out that increasingly attractive interactions, represented by partially concave local potential in the Lagrangian, may lead to the degeneracy of the blocked, renormalized action at the gliding cutoff scale by tree-level renormalization. A quantum counterpart of this mechanism is presented in the two-dimensional sine-Gordon model. The presence of Quantum Censorship is conjectured which makes the loop contributions pile up during the renormalization and thereby realize an approximate semiclassical effect.
Quantum censorship in two dimensions
International Nuclear Information System (INIS)
Pangon, V.; Nagy, S.; Polonyi, J.; Sailer, K.
2010-01-01
It is pointed out that increasingly attractive interactions, represented by partially concave local potential in the Lagrangian, may lead to the degeneracy of the blocked, renormalized action at the gliding cutoff scale by tree-level renormalization. A quantum counterpart of this mechanism is presented in the two-dimensional sine-Gordon model. The presence of Quantum Censorship is conjectured which makes the loop contributions pile up during the renormalization and thereby realize an approximate semiclassical effect.
Application of Quantum Process Calculus to Higher Dimensional Quantum Protocols
Directory of Open Access Journals (Sweden)
Simon J. Gay
2014-07-01
Full Text Available We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. We have extended the quantum process calculus to describe d-dimensional quantum systems, which has not been done before. We summarise the necessary theory in the generalisation of quantum gates and Bell states and use the theory to apply the quantum process calculus CQP to quantum protocols, namely qudit teleportation and superdense coding.
Unitary Application of the Quantum Error Correction Codes
International Nuclear Information System (INIS)
You Bo; Xu Ke; Wu Xiaohua
2012-01-01
For applying the perfect code to transmit quantum information over a noise channel, the standard protocol contains four steps: the encoding, the noise channel, the error-correction operation, and the decoding. In present work, we show that this protocol can be simplified. The error-correction operation is not necessary if the decoding is realized by the so-called complete unitary transformation. We also offer a quantum circuit, which can correct the arbitrary single-qubit errors.
Euclidean and Lorentzian Quantum Gravity – Lessons from Two Dimensions
Ambjørn, J.; Loll, R.; Nielsen, J. L.; Rolf, J.
1998-01-01
No theory of four-dimensional quantum gravity exists as yet. In this situation the two-dimensional theory, which can be analyzed by conventional field-theoretical methods, can serve as a toy model for studying some aspects of quantum gravity. It represents one of the rare settings in a
One-dimensional quantum walk with a moving boundary
International Nuclear Information System (INIS)
Kwek, Leong Chuan; Setiawan
2011-01-01
Quantum walks are interesting models with potential applications to quantum algorithms and physical processes such as photosynthesis. In this paper, we study two models of one-dimensional quantum walks, namely, quantum walks with a moving absorbing wall and quantum walks with one stationary and one moving absorbing wall. For the former, we calculate numerically the survival probability, the rate of change of average position, and the rate of change of standard deviation of the particle's position in the long time limit for different wall velocities. Moreover, we also study the asymptotic behavior and the dependence of the survival probability on the initial particle's state. While for the latter, we compute the absorption probability of the right stationary wall for different velocities and initial positions of the left wall boundary. The results for these two models are compared with those obtained for the classical model. The difference between the results obtained for the quantum and classical models can be attributed to the difference in the probability distributions.
Quantum-corrected transient analysis of plasmonic nanostructures
Uysal, Ismail Enes; Ulku, Huseyin Arda; Sajjad, Muhammad; Singh, Nirpendra; Schwingenschlö gl, Udo; Bagci, Hakan
2017-01-01
A time domain surface integral equation (TD-SIE) solver is developed for quantum-corrected analysis of transient electromagnetic field interactions on plasmonic nanostructures with sub-nanometer gaps. “Quantum correction” introduces an auxiliary
Quantum interest in (3+1)-dimensional Minkowski space
International Nuclear Information System (INIS)
Abreu, Gabriel; Visser, Matt
2009-01-01
The so-called 'quantum inequalities', and the 'quantum interest conjecture', use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a timelike observer, potentially preventing the existence of exotic phenomena such as 'Alcubierre warp drives' or 'traversable wormholes'. Both the quantum inequalities and the quantum interest conjecture can be reduced to statements concerning the existence or nonexistence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple variational proof of one version of the quantum interest conjecture in (3+1)-dimensional Minkowski space.
Two-dimensional hole systems in indium-based quantum well heterostructures
Energy Technology Data Exchange (ETDEWEB)
Loher, Josef
2016-08-01
The complex spin-orbit interaction (SOI) of two-dimensional hole gas (2DHG) systems - the relativistic coupling of the hole spin degree of freedom to their movement in an electric field - is of fundamental interest in spin physics due to its key role for spin manipulation in spintronic devices. In this work, we were able to evaluate the tunability of Rashba-SOI-related parameters in the 2DHG system of InAlAs/InGaAs/InAs:Mn quantum well heterostructures experimentally by analyzing the hole density evolution of quantum interference effects at low magnetic fields. We achieved to cover a significant range of hole densities by the joint action of the variation of the manganese modulation doping concentration during molecular beam epitaxy and external field-effect-mediated manipulation of the 2D carrier density in Hall bar devices by a metallic topgate. Within these magnetotransport experiments, a reproducible phenomenon of remarkable robustness emerged in the transverse Hall magnetoresistivity of the indium 2DHG systems which are grown on a special InAlAs step-graded metamorphic buffer layer structure to compensate crystal lattice mismatch. As a consequence of the strain relaxation process, these material systems are characterized by anisotropic properties along different crystallographic directions. We identify a puzzling offset phenomenon in the zero-field Hall magnetoresistance and demonstrate it to be a universal effect in systems with spatially anisotropic transport properties.
Gravity induced corrections to quantum mechanical wave functions
International Nuclear Information System (INIS)
Singh, T.P.
1990-03-01
We perform a semiclassical expansion in the Wheeler-DeWitt equation, in powers of the gravitational constant. We then show that quantum gravitational fluctuations can provide a correction to the wave-functions which are solutions of the Schroedinger equation for matter. This also implies a correction to the expectation values of quantum mechanical observables. (author). 6 refs
Two novel classes of solvable many-body problems of goldfish type with constraints
Energy Technology Data Exchange (ETDEWEB)
Calogero, F [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , 00185 Rome (Italy); Gomez-Ullate, D [Departamento de Fisica Teorica II, Universidad Complutense, 28040 Madrid (Spain)
2007-05-18
Two novel classes of many-body models with nonlinear interactions 'of goldfish type' are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints), i.e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited, i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.
On low-energy effective action in three-dimensional = 2 and = 4 supersymmetric electrodynamics
Buchbinder, I. L.; Merzlikin, B. S.; Samsonov, I. B.
2013-11-01
We discuss general structure of low-energy effective actions in = 2 and = 4 three-dimensional supersymmetric electrodynamics (SQED) in gauge superfield sector. There are specific terms in the effective action having no four-dimensional analogs. Some of these terms are responsible for the moduli space metric in the Coulomb branch of the theory. We find two-loop quantum corrections to the moduli space metric in the = 2 SQED and show that in the = 4 SQED the moduli space does not receive two-loop quantum corrections.
Vanishing quantum vacuum energy in eleven-dimensional supergravity on the round seven-sphere
International Nuclear Information System (INIS)
Inami, T.; Yamagishi, K.
1984-01-01
Quantum corrections to the vacuum energy are evaluated at one-loop order in eleven-dimensional supergravity on the round seven-sphere S 7 and are shown to vanish. The cancellation is also shown for all ultraviolet poles at z = 11/2, 10/2,..., corresponding to divergences of eleventh and lower powers of momentum cut-off Λ. (orig.)
First order correction to quasiclassical scattering amplitude
International Nuclear Information System (INIS)
Kuz'menko, A.V.
1978-01-01
First order (with respect to h) correction to quasiclassical with the aid of scattering amplitude in nonrelativistic quantum mechanics is considered. This correction is represented by two-loop diagrams and includes the double integrals. With the aid of classical equations of motion, the sum of the contributions of the two-loop diagrams is transformed into the expression which includes one-dimensional integrals only. The specific property of the expression obtained is that the integrand does not possess any singularities in the focal points of the classical trajectory. The general formula takes much simpler form in the case of one-dimensional systems
Strong Coupling Corrections in Quantum Thermodynamics
Perarnau-Llobet, M.; Wilming, H.; Riera, A.; Gallego, R.; Eisert, J.
2018-03-01
Quantum systems strongly coupled to many-body systems equilibrate to the reduced state of a global thermal state, deviating from the local thermal state of the system as it occurs in the weak-coupling limit. Taking this insight as a starting point, we study the thermodynamics of systems strongly coupled to thermal baths. First, we provide strong-coupling corrections to the second law applicable to general systems in three of its different readings: As a statement of maximal extractable work, on heat dissipation, and bound to the Carnot efficiency. These corrections become relevant for small quantum systems and vanish in first order in the interaction strength. We then move to the question of power of heat engines, obtaining a bound on the power enhancement due to strong coupling. Our results are exemplified on the paradigmatic non-Markovian quantum Brownian motion.
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, Abhik; Janaki, M. S. [Saha Institute of Nuclear Physics, Calcutta (India); Bose, Anirban [Serampore College, West Bengal (India)
2014-07-15
Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.
Methodology for bus layout for topological quantum error correcting codes
Energy Technology Data Exchange (ETDEWEB)
Wosnitzka, Martin; Pedrocchi, Fabio L.; DiVincenzo, David P. [RWTH Aachen University, JARA Institute for Quantum Information, Aachen (Germany)
2016-12-15
Most quantum computing architectures can be realized as two-dimensional lattices of qubits that interact with each other. We take transmon qubits and transmission line resonators as promising candidates for qubits and couplers; we use them as basic building elements of a quantum code. We then propose a simple framework to determine the optimal experimental layout to realize quantum codes. We show that this engineering optimization problem can be reduced to the solution of standard binary linear programs. While solving such programs is a NP-hard problem, we propose a way to find scalable optimal architectures that require solving the linear program for a restricted number of qubits and couplers. We apply our methods to two celebrated quantum codes, namely the surface code and the Fibonacci code. (orig.)
Asymptotics for Two-dimensional Atoms
DEFF Research Database (Denmark)
Nam, Phan Thanh; Portmann, Fabian; Solovej, Jan Philip
2012-01-01
We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E^{\\TF}(\\lambd......We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E......^{\\TF}(\\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\\rm H}\\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\\to \\infty$, which is contrary to the expected behavior of three-dimensional atoms....
Higher dimensional quantum Hall effect as A-class topological insulator
Energy Technology Data Exchange (ETDEWEB)
Hasebe, Kazuki, E-mail: khasebe@stanford.edu
2014-09-15
We perform a detail study of higher dimensional quantum Hall effects and A-class topological insulators with emphasis on their relations to non-commutative geometry. There are two different formulations of non-commutative geometry for higher dimensional fuzzy spheres: the ordinary commutator formulation and quantum Nambu bracket formulation. Corresponding to these formulations, we introduce two kinds of monopole gauge fields: non-abelian gauge field and antisymmetric tensor gauge field, which respectively realize the non-commutative geometry of fuzzy sphere in the lowest Landau level. We establish connection between the two types of monopole gauge fields through Chern–Simons term, and derive explicit form of tensor monopole gauge fields with higher string-like singularity. The connection between two types of monopole is applied to generalize the concept of flux attachment in quantum Hall effect to A-class topological insulator. We propose tensor type Chern–Simons theory as the effective field theory for membranes in A-class topological insulators. Membranes turn out to be fractionally charged objects and the phase entanglement mediated by tensor gauge field transforms the membrane statistics to be anyonic. The index theorem supports the dimensional hierarchy of A-class topological insulator. Analogies to D-brane physics of string theory are discussed too.
A two-dimensional matrix correction for off-axis portal dose prediction errors
International Nuclear Information System (INIS)
Bailey, Daniel W.; Kumaraswamy, Lalith; Bakhtiari, Mohammad; Podgorsak, Matthew B.
2013-01-01
Purpose: This study presents a follow-up to a modified calibration procedure for portal dosimetry published by Bailey et al. [“An effective correction algorithm for off-axis portal dosimetry errors,” Med. Phys. 36, 4089–4094 (2009)]. A commercial portal dose prediction system exhibits disagreement of up to 15% (calibrated units) between measured and predicted images as off-axis distance increases. The previous modified calibration procedure accounts for these off-axis effects in most regions of the detecting surface, but is limited by the simplistic assumption of radial symmetry. Methods: We find that a two-dimensional (2D) matrix correction, applied to each calibrated image, accounts for off-axis prediction errors in all regions of the detecting surface, including those still problematic after the radial correction is performed. The correction matrix is calculated by quantitative comparison of predicted and measured images that span the entire detecting surface. The correction matrix was verified for dose-linearity, and its effectiveness was verified on a number of test fields. The 2D correction was employed to retrospectively examine 22 off-axis, asymmetric electronic-compensation breast fields, five intensity-modulated brain fields (moderate-high modulation) manipulated for far off-axis delivery, and 29 intensity-modulated clinical fields of varying complexity in the central portion of the detecting surface. Results: Employing the matrix correction to the off-axis test fields and clinical fields, predicted vs measured portal dose agreement improves by up to 15%, producing up to 10% better agreement than the radial correction in some areas of the detecting surface. Gamma evaluation analyses (3 mm, 3% global, 10% dose threshold) of predicted vs measured portal dose images demonstrate pass rate improvement of up to 75% with the matrix correction, producing pass rates that are up to 30% higher than those resulting from the radial correction technique alone. As
Two quantum Simpson’s paradoxes
International Nuclear Information System (INIS)
Paris, Matteo G A
2012-01-01
The so-called Simpson’s ‘paradox’, or Yule–Simpson (YS) effect, occurs in classical statistics when the correlations that are present among different sets of samples are reversed if the sets are combined together, thus ignoring one or more lurking variables. Here we illustrate the occurrence of two analog effects in quantum measurements. The first, which we term the quantum–classical YS effect, may occur with quantum limited measurements and with lurking variables coming from the mixing of states, whereas the second, here referred to as the quantum–quantum YS effect, may take place when coherent superpositions of quantum states are allowed. By analyzing quantum measurements on low-dimensional systems (qubits and qutrits), we show that the two effects may occur independently and that the quantum–quantum YS effect is more likely to occur than the corresponding quantum–classical one. We also found that there exist classes of superposition states for which the quantum–classical YS effect cannot occur for any measurement and, at the same time, the quantum–quantum YS effect takes place in a consistent fraction of the possible measurement settings. The occurrence of the effect in the presence of partial coherence is discussed as well as its possible implications for quantum hypothesis testing. (fast track communication)
Mass spectrum of the two dimensional lambdaphi4-1/4phi2-μphi quantum field model
International Nuclear Information System (INIS)
Imbrie, J.Z.
1980-01-01
It is shown that r-particle irreducible kernels in the two-dimensional lambdaphi 4 -1/4phi 2 -μphi quantum field theory have (r+1)-particle decay for vertical stroke μ vertical stroke 2 << 1. As a consequence there is an upper mass gap and, in the subspace of two-particle states, a bound state. The proof extends Spencer's expansion to handle fluctuations between the two wells of the classical potential. A new method for resumming the low temperature cluster expansion is introduced. (orig.)
Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.
Liu, Jingfeng; Zhou, Ming; Yu, Zongfu
2016-09-15
A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.
Multichain Mean-Field Theory of Quasi-One-Dimensional Quantum Spin Systems
International Nuclear Information System (INIS)
Sandvik, A.W.
1999-01-01
A multichain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C 0 is modeled by a number of neighboring chains C δ , δ=±1, hor-ellipsis,± , with the edge chains C ±n coupled to a staggered field. Using a quantum Monte Carlo method, the effective (2n+1) -chain Hamiltonian is solved self-consistently for n up to 4 . The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization M for small interchain couplings α behaves as M∼√(α) enhanced by a multiplicative logarithmic correction. copyright 1999 The American Physical Society
Solvable model of quantum microcanonical states
International Nuclear Information System (INIS)
Bender, Carl M; Brody, Dorje C; Hook, Daniel W
2005-01-01
This letter examines the consequences of a recently proposed modification of the postulate of equal a priori probability in quantum statistical mechanics. This modification, called the quantum microcanonical postulate (QMP), asserts that for a system in microcanonical equilibrium all pure quantum states having the same energy expectation value are realized with equal probability. A simple model of a quantum system that obeys the QMP and that has a nondegenerate spectrum with equally spaced energy eigenvalues is studied. This model admits a closed-form expression for the density of states in terms of the energy eigenvalues. It is shown that in the limit as the number of energy levels approaches infinity, the expression for the density of states converges to a δ function centred at the intermediate value (E max + E min )/2 of the energy. Determining this limit requires an elaborate asymptotic study of an infinite sum whose terms alternate in sign. (letter to the editor)
Uysal, Ismail Enes
2016-10-01
Plasmonic structures are utilized in many applications ranging from bio-medicine to solar energy generation and transfer. Numerical schemes capable of solving equations of classical electrodynamics have been the method of choice for characterizing scattering properties of such structures. However, as dimensions of these plasmonic structures reduce to nanometer scale, quantum mechanical effects start to appear. These effects cannot be accurately modeled by available classical numerical methods. One of these quantum effects is the tunneling, which is observed when two structures are located within a sub-nanometer distance of each other. At these small distances electrons “jump" from one structure to another and introduce a path for electric current to flow. Classical equations of electrodynamics and the schemes used for solving them do not account for this additional current path. This limitation can be lifted by introducing an auxiliary tunnel with material properties obtained using quantum models and applying a classical solver to the structures connected by this auxiliary tunnel. Early work on this topic focused on quantum models that are generated using a simple one-dimensional wave function to find the tunneling probability and assume a simple Drude model for the permittivity of the tunnel. These tunnel models are then used together with a classical frequency domain solver. In this thesis, a time domain surface integral equation solver for quantum corrected analysis of transient plasmonic interactions is proposed. This solver has several advantages: (i) As opposed to frequency domain solvers, it provides results at a broad band of frequencies with a single simulation. (ii) As opposed to differential equation solvers, it only discretizes surfaces (reducing number of unknowns), enforces the radiation condition implicitly (increasing the accuracy), and allows for time step selection independent of spatial discretization (increasing efficiency). The quantum model
The Rashba and Dresselhaus spin-orbit interactions in a two-dimensional quantum pseudo-dot system
Akbari, M.; Rezaei, G.; Khordad, R.
2017-01-01
We study the impact of the spin-orbit coupling due to both structure and crystal inversion asymmetry and external magnetic field on the level structure in a two-dimensional quantum pseudo-dot. It is demonstrated that, both the spin-orbit interactions and magnetic field strength have a great influence on energy eigenvalues of the system. Also, we found that an increase in magnetic field enhances the spin-orbit coupling strength. This phenomena leads to increase the energy eigenvalues and energy splitting due to the spin-orbit coupling.
Quantum loop corrections of a charged de Sitter black hole
Naji, J.
2018-03-01
A charged black hole in de Sitter (dS) space is considered and logarithmic corrected entropy used to study its thermodynamics. Logarithmic corrections of entropy come from thermal fluctuations, which play a role of quantum loop correction. In that case we are able to study the effect of quantum loop on black hole thermodynamics and statistics. As a black hole is a gravitational object, it helps to obtain some information about the quantum gravity. The first and second laws of thermodynamics are investigated for the logarithmic corrected case and we find that it is only valid for the charged dS black hole. We show that the black hole phase transition disappears in the presence of logarithmic correction.
Black Holes, Holography, and Quantum Error Correction
CERN. Geneva
2017-01-01
How can it be that a local quantum field theory in some number of spacetime dimensions can "fake" a local gravitational theory in a higher number of dimensions? How can the Ryu-Takayanagi Formula say that an entropy is equal to the expectation value of a local operator? Why do such things happen only in gravitational theories? In this talk I will explain how a new interpretation of the AdS/CFT correspondence as a quantum error correcting code provides satisfying answers to these questions, and more generally gives a natural way of generating simple models of the correspondence. No familiarity with AdS/CFT or quantum error correction is assumed, but the former would still be helpful.
International Nuclear Information System (INIS)
Pang Chaoyang; Hu Benqiong
2008-01-01
The discrete Fourier transform (DFT) is the base of modern signal processing. 1-dimensional fast Fourier transform (ID FFT) and 2D FFT have time complexity O (N log N) and O (N 2 log N) respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. One-dimensional quantum DFT (ID QDFT) and two-dimensional quantum DFT (2D QDFT) are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, ID and 2D QDFT have time complexity O(√N) and O (N) respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible. (general)
Topological order and memory time in marginally-self-correcting quantum memory
Siva, Karthik; Yoshida, Beni
2017-03-01
We examine two proposals for marginally-self-correcting quantum memory: the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their Gibbs ensembles can be prepared via a short-depth quantum circuit from classical ensembles. Our proof technique naturally gives rise to the notion of free energy associated with excitations. Further, we develop a framework for an ergodic decomposition of Davies generators in CSS codes which enables formal reduction to simpler classical memory problems. We then show that memory time in the welded code is doubly exponential in inverse temperature via the Peierls argument. These results introduce further connections between thermal topological order and self-correction from the viewpoint of free energy and quantum circuit depth.
Two numerical methods for the solution of two-dimensional eddy current problems
International Nuclear Information System (INIS)
Biddlecombe, C.S.
1978-07-01
A general method for the solution of eddy current problems in two dimensions - one component of current density and two of magnetic field, is reported. After examining analytical methods two numerical methods are presented. Both solve the two dimensional, low frequency limit of Maxwell's equations for transient eddy currents in conducting material, which may be permeable, in the presence of other non-conducting permeable material. Both solutions are expressed in terms of the magnetic vector potential. The first is an integral equation method, using zero order elements in the discretisation of the unknown source regions. The other is a differential equation method, using a first order finite element mesh, and the Galerkin weighted residual procedure. The resulting equations are solved as initial-value problems. Results from programs based on each method are presented showing the power and limitations of the methods and the range of problems solvable. The methods are compared and recommendations are made for choosing between them. Suggestions are made for improving both methods, involving boundary integral techniques. (author)
He, Ling Yan; Wang, Tie-Jun; Wang, Chuan
2016-07-11
High-dimensional quantum system provides a higher capacity of quantum channel, which exhibits potential applications in quantum information processing. However, high-dimensional universal quantum logic gates is difficult to achieve directly with only high-dimensional interaction between two quantum systems and requires a large number of two-dimensional gates to build even a small high-dimensional quantum circuits. In this paper, we propose a scheme to implement a general controlled-flip (CF) gate where the high-dimensional single photon serve as the target qudit and stationary qubits work as the control logic qudit, by employing a three-level Λ-type system coupled with a whispering-gallery-mode microresonator. In our scheme, the required number of interaction times between the photon and solid state system reduce greatly compared with the traditional method which decomposes the high-dimensional Hilbert space into 2-dimensional quantum space, and it is on a shorter temporal scale for the experimental realization. Moreover, we discuss the performance and feasibility of our hybrid CF gate, concluding that it can be easily extended to a 2n-dimensional case and it is feasible with current technology.
New mixed quantum/semiclassical propagation method
International Nuclear Information System (INIS)
Antoniou, Dimitri; Gelman, David; Schwartz, Steven D.
2007-01-01
The authors developed a new method for calculating the quantum evolution of multidimensional systems, for cases in which the system can be assumed to consist of a quantum subsystem and a bath subsystem of heavier atoms. The method combines two ideas: starting from a simple frozen Gaussian description of the bath subsystem, then calculate quantum corrections to the propagation of the quantum subsystem. This follows from recent work by one of them, showing how one can calculate corrections to approximate evolution schemes, even when the Hamiltonian that corresponds to these approximate schemes is unknown. Then, they take the limit in which the width of the frozen Gaussians approaches zero, which makes the corrections to the evolution of the quantum subsystem depend only on classical bath coordinates. The test calculations they present use low-dimensional systems, in which comparison to exact quantum dynamics is feasible
Real-space mapping of a disordered two-dimensional electron system in the quantum Hall regime
International Nuclear Information System (INIS)
Hashimoto, K; Hirayama, Y; Wiebe, J; Wiesendanger, R; Inaoka, T; Morgenstern, M
2011-01-01
By using scanning tunnelling spectroscopy, we study the influence of potential disorder on an adsorbate-induced two-dimensional electron system in the integer quantum Hall regime. The real-space imaged local density of states exhibits transition from localized drift states encircling the potential minima to another type of localized drift states encircling the potential maxima. While the former states show regular round shapes, the latter have irregular-shaped patterns. This difference is induced by different sources for the potential minima and maxima, i.e., substrate donors and an inhomogeneous distribution of the adsorbates, respectively.
The Lambert-W step-potential – an exactly solvable confluent hypergeometric potential
Energy Technology Data Exchange (ETDEWEB)
Ishkhanyan, A.M., E-mail: aishkhanyan@gmail.com [Institute for Physical Research, NAS of Armenia, 0203 Ashtarak (Armenia); Armenian State Pedagogical University, 0010 Yerevan (Armenia); Institute of Physics and Technology, National Research Tomsk Polytechnic University, Tomsk 634050 (Russian Federation)
2016-02-15
We present an asymmetric step–barrier potential for which the one-dimensional stationary Schrödinger equation is exactly solved in terms of the confluent hypergeometric functions. The potential is given in terms of the Lambert W-function, which is an implicitly elementary function also known as the product logarithm. We present the general solution of the problem and consider the quantum reflection at transmission of a particle above this potential barrier. Compared with the abrupt-step and hyperbolic tangent potentials, which are reproduced by the Lambert potential in certain parameter and/or variable variation regions, the reflection coefficient is smaller because of the lesser steepness of the potential on the particle incidence side. Presenting the derivation of the Lambert potential we show that this is a four-parametric sub-potential of a more general five-parametric one also solvable in terms of the confluent hypergeometric functions. The latter potential, however, is a conditionally integrable one. Finally, we show that there exists one more potential the solution for which is written in terms of the derivative of a bi-confluent Heun function. - Highlights: • We introduce an asymmetric step-barrier potential for which the 1D Schrödinger equation is exactly solved in terms of confluent hypergeometric functions. • The potential is given in terms of the Lambert-function, which is an implicitly elementary function also known as the product logarithm. • This is a four-parametric specification of a more general five-parametric potential also solvable in terms of the confluent hypergeometric functions. • There exists one more potential the solution for which is written in terms of the derivative of a bi-confluent Heun function.
Energy Technology Data Exchange (ETDEWEB)
Nakra Mohajer, Soukaina; El Harouny, El Hassan [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); Ibral, Asmaa [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); El Khamkhami, Jamal [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); and others
2016-09-15
Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.
International Nuclear Information System (INIS)
Nakra Mohajer, Soukaina; El Harouny, El Hassan; Ibral, Asmaa; El Khamkhami, Jamal
2016-01-01
Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.
Quantum Mechanics and Black Holes in Four-Dimensional String Theory
Ellis, Jonathan Richard; Nanopoulos, Dimitri V
1992-01-01
In previous papers we have shown how strings in a two-dimensional target space reconcile quantum mechanics with general relativity, thanks to an infinite set of conserved quantum numbers, ``W-hair'', associated with topological soliton-like states. In this paper we extend these arguments to four dimensions, by considering explicitly the case of string black holes with radial symmetry. The key infinite-dimensional W-symmetry is associated with the $\\frac{SU(1,1)}{U(1)}$ coset structure of the dilaton-graviton sector that is a model-independent feature of spherically symmetric four-dimensional strings. Arguments are also given that the enormous number of string {\\it discrete (topological)} states account for the maintenance of quantum coherence during the (non-thermal) stringy evaporation process, as well as quenching the large Hawking-Bekenstein entropy associated with the black hole. Defining the latter as the measure of the loss of information for an observer at infinity, who - ignoring the higher string qua...
Activation of zero-error classical capacity in low-dimensional quantum systems
Park, Jeonghoon; Heo, Jun
2018-06-01
Channel capacities of quantum channels can be nonadditive even if one of two quantum channels has no channel capacity. We call this phenomenon activation of the channel capacity. In this paper, we show that when we use a quantum channel on a qubit system, only a noiseless qubit channel can generate the activation of the zero-error classical capacity. In particular, we show that the zero-error classical capacity of two quantum channels on qubit systems cannot be activated. Furthermore, we present a class of examples showing the activation of the zero-error classical capacity in low-dimensional systems.
Vayrynen, Jukka; Goldstein, Moshe; Glazman, Leonid
2013-03-01
Static charge disorder may create electron puddles in the bulk of a material which nominally is in the insulating state. A single puddle - quantum dot - coupled to the helical edge of a two-dimensional topological insulator enhances the electron backscattering within the edge. The backscattering rate increases with the electron dwelling time in the dot. While remaining inelastic, the backscattering off a dot may be far more effective than the proposed earlier inelastic processes involving a local scatterer with no internal structure. We find the temperature dependence of the dot-induced correction to the universal conductance of the edge. In addition to the single-dot effect, we calculate the classical temperature-independent conductance correction caused by a weakly conducting bulk. We use our theory to assess the effect of static charge fluctuations in a heterostructure on the edge electron transport in a two-dimensional topological insulator. The work at Yale University is supported by NSF DMR Grant No. 1206612 and the Simons Foundation.
Coulomb systems seen as critical systems: Finite-size effects in two dimensions
International Nuclear Information System (INIS)
Jancovici, B.; Manificat, G.; Pisani, C.
1994-01-01
It is known that the free energy at criticality of a finite two-dimensional system of characteristic size L has in general a term which behaves like log L as L → ∞; the coefficient of this term is universal. There are solvable models of two-dimensional classical Coulomb systems which exhibit the same finite-size correction (except for its sign) although the particle correlations are short-ranged, i.e., noncritical. Actually, the electrical potential and electrical field correlations are critical at all temperatures (as long as the Coulomb system is a conductor), as a consequence of the perfect screening property of Coulomb systems. This is why Coulomb systems have to exhibit critical finite-size effects
Two-dimensional thermofield bosonization
International Nuclear Information System (INIS)
Amaral, R.L.P.G.; Belvedere, L.V.; Rothe, K.D.
2005-01-01
The main objective of this paper was to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real-time formalism of Thermofield Dynamics. Formally, the results parallel those of the T = 0 case. The well-known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. To emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real-time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized
Quantum Finance: The Finite Dimensional Case
Chen, Zeqian
2001-01-01
In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As examples, the quantum model of binomial markets is studied. We show that this quantum model ceases to pose the paradox which appears in the classical model of the binomial market. Furthermore, we re-deduce the Cox-Ross-Rubinstein binomial option pricing form...
Quantum-corrected transient analysis of plasmonic nanostructures
Uysal, Ismail Enes
2017-03-08
A time domain surface integral equation (TD-SIE) solver is developed for quantum-corrected analysis of transient electromagnetic field interactions on plasmonic nanostructures with sub-nanometer gaps. “Quantum correction” introduces an auxiliary tunnel to support the current path that is generated by electrons tunneled between the nanostructures. The permittivity of the auxiliary tunnel and the nanostructures is obtained from density functional theory (DFT) computations. Electromagnetic field interactions on the combined structure (nanostructures plus auxiliary tunnel connecting them) are computed using a TD-SIE solver. Time domain samples of the permittivity and the Green function required by this solver are obtained from their frequency domain samples (generated from DFT computations) using a semi-analytical method. Accuracy and applicability of the resulting quantum-corrected solver scheme are demonstrated via numerical examples.
Solvable lattice models with minimal and nonunitary critical behaviour in two dimensions
International Nuclear Information System (INIS)
Riggs, H.; Chicago Univ., IL
1989-01-01
The exact local height probabilities found by Forrester and Baxter for a series of solvable lattice models in two dimensions are written in terms of nonunitary Virasoro characters and modifications of unitary A 1 (1) affine Lie algebra characters directly related to nonunitary but rational-level A 1 (1) characters. The relation between these results and a rational-level GKO decomposition is given. The off-critical lattice origin of the Virasoro characters and the role of the embedding diagram null vectors in the CTM eigenspace is described. Suggestions for the definition of rational and nonunitary models corresponding to arbitrary G/H cosets are given. (orig.)
Energy Technology Data Exchange (ETDEWEB)
El-Menoufi, Basem Kamal [Department of Physics, University of Massachusetts,Amherst, MA 01003 (United States)
2016-05-05
In the context of effective field theory, we consider quantum gravity with minimally coupled massless particles. Fixing the background geometry to be of the Kerr-Schild type, we fully determine the one-loop effective action of the theory whose finite non-local part is induced by the long-distance portion of quantum loops. This is accomplished using the non-local expansion of the heat kernel in addition to a non-linear completion technique through which the effective action is expanded in gravitational curvatures. Via Euclidean methods, we identify a logarithmic correction to the Bekenstein-Hawking entropy of Schwarzschild black hole. Using dimensional transmutation the result is shown to exhibit an interesting interplay between the UV and IR properties of quantum gravity.
The discretized Schroedinger equation and simple models for semiconductor quantum wells
International Nuclear Information System (INIS)
Boykin, Timothy B; Klimeck, Gerhard
2004-01-01
The discretized Schroedinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schroedinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schroedinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one
Quantum interference of ballistic carriers in one-dimensional semiconductor rings
International Nuclear Information System (INIS)
Bagraev, N.T.; Buravlev, A.D.; Klyachkin, L.E.; Malyarenko, A.M.; Ivanov, V.K.; Rykov, S.A.; Shelykh, I.A.
2000-01-01
Quantum interference of ballistic carriers has been studied for the first time, using one-dimensional rings formed by quantum wire pairs in self-assembled silicon quantum wells. Energy dependencies of the transmission coefficient is calculated as a function of the length and modulation of the quantum wire pairs separated by a unified drain-source system or the quantum point contacts. The quantum conductance is predicted to be increased by a factor of four using the unified drain-source system as a result of the quantum interference. Theoretical dependencies are revealed by the quantum conductance oscillations created by the deviations of both the drain-source voltage and external magnetic field inside the silicon one-dimensional rings. The results obtained put forward a basis to create the Aharonov-Bohm interferometer using the silicon one-dimensional ring [ru
Extensions of conformal symmetry in two-dimensional quantum field theory
International Nuclear Information System (INIS)
Schoutens, C.J.M.
1989-01-01
Conformal symmetry extensions in a two-dimensional quantum field theory are the main theme of the work presented in this thesis. After a brief exposition of the formalism for conformal field theory, the motivation for studying extended symmetries in conformal field theory is presented in some detail. Supersymmetric extensions of conformal symmetry are introduced. An overview of the algebraic superconformal symmetry is given. The relevance of higher-spin bosonic extensions of the Virasoro algebra in relation to the classification program for so-called rational conformal theories is explained. The construction of a large class of bosonic extended algebras, the so-called Casimir algebras, are presented. The representation theory of these algebras is discussed and a large class of new unitary models is identified. The superspace formalism for O(N)-extended superconformal quantum field theory is presented. It is shown that such theories exist for N ≤ 4. Special attention is paid to the case N = 4 and it is shown that the allowed central charges are c(n + ,n - ) = 6n + n - /(n + ,n - ), where n + and n - are positive integers. A different class of so(N)-extended superconformal algebras is analyzed. The representation theory is studied and it is established that certain free field theories provide realizations of the algebras with level S = 1. Finally the so-called BRST construction for extended conformal algebras is considered. A nilpotent BRST charge is constructed for a large class of algebras, which contains quadratically nonlinear algebras that fall outside the traditional class if finitely generated Lie (super)algebras. The results are especially relevant for the construction of string models based on extended conformal symmetry. (author). 118 refs.; 7 tabs
A surface code quantum computer in silicon
Hill, Charles D.; Peretz, Eldad; Hile, Samuel J.; House, Matthew G.; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y.; Hollenberg, Lloyd C. L.
2015-01-01
The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel—posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited. PMID:26601310
A surface code quantum computer in silicon.
Hill, Charles D; Peretz, Eldad; Hile, Samuel J; House, Matthew G; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y; Hollenberg, Lloyd C L
2015-10-01
The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited.
Jana, Subrata; Samal, Prasanjit
2018-01-01
The behaviors of the positive definite Kohn-Sham kinetic energy density near the origin and at the asymptotic region play a major role in designing meta-generalized gradient approximations (meta-GGAs) for exchange in low-dimensional quantum systems. It is shown that near the origin of the parabolic quantum dot, the Kohn-Sham kinetic energy differs from its von Weizsäcker counterpart due to the p orbital contributions, whereas in the asymptotic region, the difference between the above two kinetic energy densities goes as ˜ρ/(r ) r2 . All these behaviors have been explored using the two-dimensional isotropic quantum harmonic oscillator as a test case. Several meta-GGA ingredients are then studied by making use of the above findings. Also, the asymptotic conditions for the exchange energy density and the potential at the meta-GGA level are proposed using the corresponding behaviors of the two kinetic energy densities.
Supersymmetric quantum mechanics in three-dimensional space, 1
International Nuclear Information System (INIS)
Ui, Haruo
1984-01-01
As a direct generalization of the model of supersymmetric quantum mechanics by Witten, which describes the motion of a spin one-half particle in the one-dimensional space, we construct a model of the supersymmetric quantum mechanics in the three-dimensional space, which describes the motion of a spin one-half particle in central and spin-orbit potentials in the context of the nonrelativistic quantum mechanics. With the simplest choice of the (super) potential, this model is shown to reduce to the model of the harmonic oscillator plus constant spin-orbit potential of unit strength of both positive and negative signs, which was studied in detail in our recent paper in connection with ''accidental degeneracy'' as well as the ''graded groups''. This simplest model is discussed in some detail as an example of the three-dimensional supersymmetric quantum mechanical system, where the supersymmetry is an exact symmetry of the system. More general choice of a polynomial superpotential is also discussed. It is shown that the supersymmetry cannot be spontaneously broken for any polynomial superpotential in our three-dimensional model; this result is contrasted to the corresponding one in the one-dimensional model. (author)
General solution of the Dirac equation for quasi-two-dimensional electrons
Energy Technology Data Exchange (ETDEWEB)
Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2016-06-15
The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.
Andreev, Pavel A.
2018-04-01
Two kinds of quantum electrodynamic radiative corrections to electromagnetic interactions and their influence on the properties of highly dense quantum plasmas are considered. Linear radiative correction to the Coulomb interaction is considered. Its contribution in the spectrum of the Langmuir waves is presented. The second kind of radiative corrections are related to the nonlinearity of the Maxwell equations for the strong electromagnetic field. Their contribution in the spectrum of transverse waves of magnetized plasmas is briefly discussed. At the consideration of the Langmuir wave spectrum, we included the effect of different distributions of the spin-up and spin-down electrons revealing in the Fermi pressure shift.
Uysal, Ismail Enes
2015-10-26
Analysis of electromagnetic interactions on nanodevices can oftentimes be carried out accurately using “traditional” electromagnetic solvers. However, if a gap of sub-nanometer scale exists between any two surfaces of the device, quantum-mechanical effects including tunneling should be taken into account for an accurate characterization of the device\\'s response. Since the first-principle quantum simulators can not be used efficiently to fully characterize a typical-size nanodevice, a quantum corrected electromagnetic model has been proposed as an efficient and accurate alternative (R. Esteban et al., Nat. Commun., 3(825), 2012). The quantum correction is achieved through an effective layered medium introduced into the gap between the surfaces. The dielectric constant of each layer is obtained using a first-principle quantum characterization of the gap with a different dimension.
Logical Qubit in a Linear Array of Semiconductor Quantum Dots
Directory of Open Access Journals (Sweden)
Cody Jones
2018-06-01
Full Text Available We design a logical qubit consisting of a linear array of quantum dots, we analyze error correction for this linear architecture, and we propose a sequence of experiments to demonstrate components of the logical qubit on near-term devices. To avoid the difficulty of fully controlling a two-dimensional array of dots, we adapt spin control and error correction to a one-dimensional line of silicon quantum dots. Control speed and efficiency are maintained via a scheme in which electron spin states are controlled globally using broadband microwave pulses for magnetic resonance, while two-qubit gates are provided by local electrical control of the exchange interaction between neighboring dots. Error correction with two-, three-, and four-qubit codes is adapted to a linear chain of qubits with nearest-neighbor gates. We estimate an error correction threshold of 10^{-4}. Furthermore, we describe a sequence of experiments to validate the methods on near-term devices starting from four coupled dots.
Deformations of infrared-conformal theories in two dimensions
Akerlund, Oscar
2014-01-01
We study two exactly solvable two-dimensional conformal models, the critical Ising model and the Sommerfield model, on the lattice. We show that finite-size effects are important and depend on the aspect ratio of the lattice. In particular, we demonstrate how to obtain the correct massless behavior from an infinite tower of finite-size-induced masses and show that it is necessary to first take the cylindrical geometry limit in order to get correct results. In the Sommerfield model we also introduce a mass deformation to measure the mass anomalous dimension, $\\gamma_m$. We find that the explicit scale breaking of the lattice setup induces corrections which must be taken into account in order to reproduce $\\gamma_m$ at the infrared fixed point. These results can be used to improve the methodology in the search for the conformal window in QCD-like theories with many flavors.
Deformed quantum double realization of the toric code and beyond
Padmanabhan, Pramod; Ibieta-Jimenez, Juan Pablo; Bernabe Ferreira, Miguel Jorge; Teotonio-Sobrinho, Paulo
2016-09-01
Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Zn and S3. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z2 phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties.
International Nuclear Information System (INIS)
Ranade, Kedar S.
2009-01-01
This PhD thesis deals with quantum-cryptographic protocols which allow general finite-dimensional quantum systems (qudits) as carriers of information in contrast to the predominantly used two-dimensional quantum systems (qubits). The main focus of investigations is the maximum tolerable error rate of such protocols and its behaviour as a function of the dimension of the information carriers. For this purpose, several concepts are introduced which allow the treatment of this problem. In particular, protocols are presented which work up to a maximum tolerate error rate, and it is shown that a wide class of protocols cannot be used for higher error rates. Among other things, it turns out that the maximum tolerable error rate for two-basis protocols increases up to 50% for high dimensions. Apart from the above-mentioned main subjects of this thesis, some other results from the field of quantum information theory are given, which were achieved during this PhD project. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Orlita, M., E-mail: milan.orlita@lncmi.cnrs.fr [Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, 38042 Grenoble (France); Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2 (Czech Republic); Faugeras, C.; Barra, A.-L.; Martinez, G.; Potemski, M. [Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, 38042 Grenoble (France); Basko, D. M. [LPMMC UMR 5493, Université Grenoble 1/CNRS, B.P. 166, 38042 Grenoble (France); Zholudev, M. S. [Laboratoire Charles Coulomb (L2C), UMR CNRS 5221, GIS-TERALAB, Université Montpellier II, 34095 Montpellier (France); Institute for Physics of Microstructures, RAS, Nizhny Novgorod GSP-105 603950 (Russian Federation); Teppe, F.; Knap, W. [Laboratoire Charles Coulomb (L2C), UMR CNRS 5221, GIS-TERALAB, Université Montpellier II, 34095 Montpellier (France); Gavrilenko, V. I. [Institute for Physics of Microstructures, RAS, Nizhny Novgorod GSP-105 603950 (Russian Federation); Mikhailov, N. N.; Dvoretskii, S. A. [A.V. Rzhanov Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090 (Russian Federation); Neugebauer, P. [Institut für Physikalische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart (Germany); Berger, C. [School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Institut Néel/CNRS-UJF BP 166, F-38042 Grenoble Cedex 9 (France); Heer, W. A. de [School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)
2015-03-21
Here, we report on a magneto-optical study of two distinct systems hosting massless fermions—two-dimensional graphene and three-dimensional HgCdTe tuned to the zero band gap condition at the point of the semiconductor-to-semimetal topological transition. Both materials exhibit, in the quantum regime, a fairly rich magneto-optical response, which is composed from a series of intra- and interband inter-Landau level resonances with for massless fermions typical √(B) dependence. The impact of the system's dimensionality and of the strength of the spin-orbit interaction on the optical response is also discussed.
El Harouny, El Hassan; Nakra Mohajer, Soukaina; Ibral, Asmaa; El Khamkhami, Jamal; Assaid, El Mahdi
2018-05-01
Eigenvalues equation of hydrogen-like off-center single donor impurity confined in polarized homogeneous hemispherical quantum dot deposited on a wetting layer, capped by insulated matrix and submitted to external uniform electric field is solved in the framework of the effective mass approximation. An infinitely deep potential is used to describe effects of quantum confinement due to conduction band offsets at surfaces where quantum dot and surrounding materials meet. Single donor ground state total and binding energies in presence of electric field are determined via two-dimensional finite difference approach and Ritz-Hassé variation principle. For the latter method, attractive coulomb correlation between electron and ionized single donor is taken into account in the expression of trial wave function. It appears that off-center single dopant binding energy, spatial extension and radial probability density are strongly dependent on hemisphere radius and single dopant position inside quantum dot. Influence of a uniform electric field is also investigated. It shows that Stark effect appears even for very small size dots and that single dopant energy shift is more significant when the single donor is near hemispherical surface.
Entanglement, decoherence and thermal relaxation in exactly solvable models
International Nuclear Information System (INIS)
Lychkovskiy, Oleg
2011-01-01
Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression describing the evolution of the reduced density matrix. This expression proves to be tractable when the combined closed system (i.e. open system plus environment) is integrable. Then we focus on comparing decoherence and thermalization timescales in the XX chain. We find that for a single spin these timescales are comparable, in contrast to what should be expected for a macroscopic body. This indicates that the process of quantum relaxation of a system with few accessible states can not be separated in two distinct stages - decoherence and thermalization. Finally, we turn to finite-size effects in the time evolution of a single spin in the XY chain. We observe three consecutive stages of the evolution: regular evolution, partial revivals, irregular (apparently chaotic) evolution. The duration of the regular stage is proportional to the number of spins in the chain. We observe a 'quiet and cold period' in the end of the regular stage, which breaks up abruptly at some threshold time.
Feynman diagrams coupled to three-dimensional quantum gravity
International Nuclear Information System (INIS)
Barrett, John W
2006-01-01
A framework for quantum field theory coupled to three-dimensional quantum gravity is proposed. The coupling with quantum gravity regulates the Feynman diagrams. One recovers the usual Feynman amplitudes in the limit as the cosmological constant tends to zero
On polynormality in finite solvable groups
Mamadou-Sadialiou-Bah
2003-01-01
In the study of the arrangement of intermediate subgroups a wide use has been made of certain properties describing the way conjugacy classes of subgroups are embedded in the groups: abnormality, pronormality, paranormality, and their weak analogues. It was proved that pronormality and abnormality coincide with their weak analogues for solvable groups. This was a generalisation of known results of Peng and Taunt for finite solvable groups. In this paper we prove a conjecture of Borevich asserting a similar result for paranormality and polynormality (which is a sort of weak paranormality). Further we show that we get a stronger result when the given subgroup is nilpotent: In a finite solvable group any nilpotent polynormal subgroup is pronormal.
On polynormality in finite solvable groups
International Nuclear Information System (INIS)
Mamadou Sadialiou Bah
2003-05-01
In the study of the arrangement of intermediate subgroups a wide use has been made of certain properties describing the way conjugacy classes of subgroups are embedded in the groups: abnormality, pronormality, paranormality, and their weak analogues. It was proved that pronormality and abnormality coincide with their weak analogues for solvable groups. This was a generalisation of known results of Peng and Taunt for finite solvable groups. In this paper we prove a conjecture of Borevich asserting a similar result for paranormality and polynormality (which is a sort of weak paranormality). Further we show that we get a stronger result when the given subgroup is nilpotent: In a finite solvable group any nilpotent polynormal subgroup is pronormal. (author)
Child abduction murder: the impact of forensic evidence on solvability.
Brown, Katherine M; Keppel, Robert D
2012-03-01
This study examined 733 child abduction murders (CAMs) occurring from 1968 to 2002 to explore the influence of forensic evidence on case solvability in CAM investigations. It was hypothesized that the presence of forensic evidence connecting the offender to the crime would enhance case solvability in murder investigations of abducted children. This study examined the impact of CAM of different types of forensic evidence and the impact of the summed total of forensic evidence items on case solvability by controlling for victim age, victim race, victim gender, and victim-offender relationship. Time and distance theoretical predictors were also included. Binomial logistic regression models were used to determine whether forensic evidence was a critical solvability factor in murder investigations of abducted children. This research indicated that, while forensic evidence increased case solvability, the impact of forensic evidence on solvability was not as important as other solvability factors examined. © 2011 American Academy of Forensic Sciences.
On-chip generation of high-dimensional entangled quantum states and their coherent control.
Kues, Michael; Reimer, Christian; Roztocki, Piotr; Cortés, Luis Romero; Sciara, Stefania; Wetzel, Benjamin; Zhang, Yanbing; Cino, Alfonso; Chu, Sai T; Little, Brent E; Moss, David J; Caspani, Lucia; Azaña, José; Morandotti, Roberto
2017-06-28
Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science. Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantum mechanics, for increasing the sensitivity of quantum imaging schemes, for improving the robustness and key rate of quantum communication protocols, for enabling a richer variety of quantum simulations, and for achieving more efficient and error-tolerant quantum computation. Integrated photonics has recently become a leading platform for the compact, cost-efficient, and stable generation and processing of non-classical optical states. However, so far, integrated entangled quantum sources have been limited to qubits (D = 2). Here we demonstrate on-chip generation of entangled qudit states, where the photons are created in a coherent superposition of multiple high-purity frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions, formed by two entangled qudits with D = 10. Furthermore, using state-of-the-art, yet off-the-shelf telecommunications components, we introduce a coherent manipulation platform with which to control frequency-entangled states, capable of performing deterministic high-dimensional gate operations. We validate this platform by measuring Bell inequality violations and performing quantum state tomography. Our work enables the generation and processing of high-dimensional quantum states in a single spatial mode.
Fauzi, Ahmad; Ratna Kawuri, Kunthi; Pratiwi, Retno
2017-01-01
Researchers of students’ conceptual change usually collects data from written tests and interviews. Moreover, reports of conceptual change often simply refer to changes in concepts, such as on a test, without any identification of the learning processes that have taken place. Research has shown that students have difficulties with vectors in university introductory physics courses and high school physics courses. In this study, we intended to explore students’ understanding of one-dimensional and two-dimensional vector in multi perspective views. In this research, we explore students’ understanding through test perspective and interviews perspective. Our research study adopted the mixed-methodology design. The participants of this research were sixty students of third semester of physics education department. The data of this research were collected by testand interviews. In this study, we divided the students’ understanding of one-dimensional vector and two-dimensional vector in two categories, namely vector skills of the addition of one-dimensionaland two-dimensional vector and the relation between vector skills and conceptual understanding. From the investigation, only 44% of students provided correct answer for vector skills of the addition of one-dimensional and two-dimensional vector and only 27% students provided correct answer for the relation between vector skills and conceptual understanding.
The Quantum Socket: Wiring for Superconducting Qubits - Part 2
Bejanin, J. H.; McConkey, T. G.; Rinehart, J. R.; Bateman, J. D.; Earnest, C. T.; McRae, C. H.; Rohanizadegan, Y.; Shiri, D.; Mariantoni, M.; Penava, B.; Breul, P.; Royak, S.; Zapatka, M.; Fowler, A. G.
Quantum computing research has reached a level of maturity where quantum error correction (QEC) codes can be executed on linear arrays of superconducting quantum bits (qubits). A truly scalable quantum computing architecture, however, based on practical QEC algorithms, requires nearest neighbor interaction between qubits on a two-dimensional array. Such an arrangement is not possible with techniques that rely on wire bonding. To address this issue, we have developed the quantum socket, a device based on three-dimensional wires that enables the control of superconducting qubits on a two-dimensional grid. In this talk, we present experimental results characterizing this type of wiring. We will show that the quantum socket performs exceptionally well for the transmission and reflection of microwave signals up to 10 GHz, while minimizing crosstalk between adjacent wires. Under realistic conditions, we measured an S21 of -5 dB at 6 GHz and an average crosstalk of -60 dB. We also describe time domain reflectometry results and arbitrary pulse transmission tests, showing that the quantum socket can be used to control superconducting qubits.
International Nuclear Information System (INIS)
Ito, K.R.
1975-01-01
The Schwinger model is considered in the Landau-gauge formalism of quantum electrodynamics. This model can be solved exactly on the assumption of no radiative corrections to the anomaly. It is found that the photon obtains a non-zero mass through the Higgs mechanism. In this case, the would-be Nambu-Goldstone boson is an associated boson which is constructed from a pair of two-component massless fermions. This would-be Nambu-Goldstone boson appears as a result of the spontaneous breaking of the gauge invariance of the first kind, and it becomes unphysical through the Higgs mechanism. However, as all the fermions themselves decouple from photons, they cannot appear as real particles in our world. (author)
Two-dimensional fractal geometry, critical phenomena and conformal invariance
International Nuclear Information System (INIS)
Duplantier, B.
1988-01-01
The universal properties of critical geometrical systems in two-dimensions (2D) like the O (n) and Potts models, are described in the framework of Coulomb gas methods and conformal invariance. The conformal spectrum of geometrical critical systems obtained is made of a discrete infinite series of scaling dimensions. Specific applications involve the fractal properties of self-avoiding walks, percolation clusters, and also some non trivial critical exponents or fractal dimensions associated with subsets of the planar Brownian motion. The statistical mechanics of the same critical models on a random 2D lattice (namely in presence of a critically-fluctuating metric, in the so-called 2D quantum gravity) is also addressed, and the above critical geometrical systems are shown to be exactly solvable in this case. The new ''gravitational'' conformal spectrum so derived is found to satisfy the recent Knizhnik, Polyakov and Zamolodchikov quadratic relation which links it to the standard conformal spectrum in the plane
Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime
Directory of Open Access Journals (Sweden)
Gianluca Calcagni
2017-10-01
Full Text Available We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.
Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime
International Nuclear Information System (INIS)
Calcagni, Gianluca; Ronco, Michele
2017-01-01
We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.
Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime
Calcagni, Gianluca; Ronco, Michele
2017-10-01
We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.
Shamim, S; Mahapatra, S; Scappucci, G; Klesse, W M; Simmons, M Y; Ghosh, A
2014-06-13
We report experimental evidence of a remarkable spontaneous time-reversal symmetry breaking in two-dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P delta layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, providing a microscopic mechanism for spontaneous lifting of the time-reversal symmetry. Our experiments suggest the emergence of a new many-body quantum state when two-dimensional electrons are confined to narrow half-filled impurity bands.
Critical behavior in two-dimensional quantum gravity and equations of motion of the string
International Nuclear Information System (INIS)
Das, S.R.; Dhar, A.; Wadia, S.R.
1990-01-01
The authors show how consistent quantization determines the renormalization of couplings in a quantum field theory coupled to gravity in two dimensions. The special status of couplings corresponding to conformally invariant matter is discussed. In string theory, where the dynamical degree of freedom of the two-dimensional metric plays the role of time in target space, these renormalization group equations are themselves the classical equations of motion. Time independent solutions, like classical vacuua, correspond to the situation in which matter is conformally invariant. Time dependent solutions, like tunnelling configurations between vacuua, correspond to special trajectories in theory space. The authors discuss an example of such a trajectory in the space containing the c ≤ 1 minimal models. The authors also discuss the connection between this work and the recent attempts to construct non-pertubative string theories based on matrix models
Infinite families of superintegrable systems separable in subgroup coordinates
International Nuclear Information System (INIS)
Lévesque, Daniel; Post, Sarah; Winternitz, Pavel
2012-01-01
A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials. (paper)
Influence of rotation and FLR corrections on selfgravitational Jeans instability in quantum plasma
International Nuclear Information System (INIS)
Jain, Shweta; Sharma, Prerana; Chhajlani, R K
2014-01-01
In the present work, the self-gravitational instability of quantum plasma is investigated including the effects of finite Larmor radius corrections (FLR) and rotation. The formulation is done employing quantum magnetohydrodynamic (QMHD) model. The plane wave solutions are employed on the linearized perturbed QMHD set of equations to obtain the general dispersion relation. The rotation is assumed only along the z- direction. The general dispersion relation is further reduced for transverse and longitudinal directions of propagation. It is found that in transverse direction of propagation the Jeans criterion is modified due to the rotation, FLR and quantum corrections while in longitudinal direction of propagation it is observed that the Jeans criterion is modified by quantum corrections only. The growth rate of perturbation is discussed numerically including the considered parameters FLR and quantum corrections. The growth rate is observed to be modified significantly due to the quantum correction and FLR effects.
Error suppression and error correction in adiabatic quantum computation: non-equilibrium dynamics
International Nuclear Information System (INIS)
Sarovar, Mohan; Young, Kevin C
2013-01-01
While adiabatic quantum computing (AQC) has some robustness to noise and decoherence, it is widely believed that encoding, error suppression and error correction will be required to scale AQC to large problem sizes. Previous works have established at least two different techniques for error suppression in AQC. In this paper we derive a model for describing the dynamics of encoded AQC and show that previous constructions for error suppression can be unified with this dynamical model. In addition, the model clarifies the mechanisms of error suppression and allows the identification of its weaknesses. In the second half of the paper, we utilize our description of non-equilibrium dynamics in encoded AQC to construct methods for error correction in AQC by cooling local degrees of freedom (qubits). While this is shown to be possible in principle, we also identify the key challenge to this approach: the requirement of high-weight Hamiltonians. Finally, we use our dynamical model to perform a simplified thermal stability analysis of concatenated-stabilizer-code encoded many-body systems for AQC or quantum memories. This work is a companion paper to ‘Error suppression and error correction in adiabatic quantum computation: techniques and challenges (2013 Phys. Rev. X 3 041013)’, which provides a quantum information perspective on the techniques and limitations of error suppression and correction in AQC. In this paper we couch the same results within a dynamical framework, which allows for a detailed analysis of the non-equilibrium dynamics of error suppression and correction in encoded AQC. (paper)
Quantum corrections for the phase diagram of systems with competing order
Silva, N. L., Jr.; Continentino, Mucio A.; Barci, Daniel G.
2018-06-01
We use the effective potential method of quantum field theory to obtain the quantum corrections to the zero temperature phase diagram of systems with competing order parameters. We are particularly interested in two different scenarios: regions of the phase diagram where there is a bicritical point, at which both phases vanish continuously, and the case where both phases coexist homogeneously. We consider different types of couplings between the order parameters, including a bilinear one. This kind of coupling breaks time-reversal symmetry and it is only allowed if both order parameters transform according to the same irreducible representation. This occurs in many physical systems of actual interest like competing spin density waves, different types of orbital antiferromagnetism, elastic instabilities of crystal lattices, vortices in a multigap SC and also applies to describe the unusual magnetism of the heavy fermion compound URu2Si2. Our results show that quantum corrections have an important effect on the phase diagram of systems with competing orders.
Quantum corrections for the phase diagram of systems with competing order.
Silva, N L; Continentino, Mucio A; Barci, Daniel G
2018-06-06
We use the effective potential method of quantum field theory to obtain the quantum corrections to the zero temperature phase diagram of systems with competing order parameters. We are particularly interested in two different scenarios: regions of the phase diagram where there is a bicritical point, at which both phases vanish continuously, and the case where both phases coexist homogeneously. We consider different types of couplings between the order parameters, including a bilinear one. This kind of coupling breaks time-reversal symmetry and it is only allowed if both order parameters transform according to the same irreducible representation. This occurs in many physical systems of actual interest like competing spin density waves, different types of orbital antiferromagnetism, elastic instabilities of crystal lattices, vortices in a multigap SC and also applies to describe the unusual magnetism of the heavy fermion compound URu 2 Si 2 . Our results show that quantum corrections have an important effect on the phase diagram of systems with competing orders.
International Nuclear Information System (INIS)
Iengo, R.; Jug, G.
1995-01-01
We investigate the phenomenon of the decay of a supercurrent through homogeneous nucleation of vortex-antivortex pairs in a two-dimensional (2D) like superconductor or superfluid by means of a quantum electrodynamic formulation for the decay of the 2D vacuum. The case in which both externally driven current and Magnus force are present is treated exactly, taking the vortex activation energy and its inertial mass as independent parameters. Quantum dissipation is included through the formulation introduced by Caldeira and Leggett. The most relevant consequence of quantum dissipation is the elimination of the threshold for vortex production due to the Magnus force. In the dissipation-dominated case, corresponding formally to the limit of zero intertial mass, an exact formula for the pair production rate is given. If however the inertial mass is strictly zero we find that vortex production is inhibited by a quantum effect related to the Magnus force. The possibility of including vortex pinning is investigated by means of an effective harmonic potential. While an additional term in the vortex activation energy can account for the effect of a finite barrier in the direction perpendicular to the current, pinning along the current depresses the role of the Magnus force in the dissipation-dominated dynamics, except for the above-mentioned quantum effect. A possible description of vortex nucleation due to the combined effects of temperature and externally driven currents is also presented along with an evaluation of the resulting voltage drop
Hanaki, Nobuyuki; Jacquemet, Nicolas; Luchini, Stéphane; Zylbersztejn, Adam
2016-01-01
Dominance solvability is one of the most straightforward solution concepts in game theory. It is based on two principles: dominance (according to which players always use their dominant strategy) and iterated dominance (according to which players always act as if others apply the principle of dominance). However, existing experimental evidence questions the empirical accuracy of dominance solvability. In this study, we study the relationships between the key facets of dominance solvability and two cognitive skills, cognitive reflection, and fluid intelligence. We provide evidence that the behaviors in accordance with dominance and one-step iterated dominance are both predicted by one's fluid intelligence rather than cognitive reflection. Individual cognitive skills, however, only explain a small fraction of the observed failure of dominance solvability. The accuracy of theoretical predictions on strategic decision making thus not only depends on individual cognitive characteristics, but also, perhaps more importantly, on the decision making environment itself.
Chiral anomaly, fermionic determinant and two dimensional models
International Nuclear Information System (INIS)
Rego Monteiro, M.A. do.
1985-01-01
The chiral anomaly in random pair dimension is analysed. This anomaly is perturbatively calculated by dimensional regularization method. A new method for non-perturbative Jacobian calculation of a general chiral transformation, 1.e., finite and non-Abelian, is developed. This method is used for non-perturbative chiral anomaly calculation, as an alternative to bosonization of two-dimensional theories for massless fermions and to study the phenomenum of fermion number fractionalization. The fermionic determinant from two-dimensional quantum chromodynamics is also studied, and calculated, exactly, as in decoupling gauge as with out reference to a particular gauge. (M.C.K.) [pt
Metrics with vanishing quantum corrections
International Nuclear Information System (INIS)
Coley, A A; Hervik, S; Gibbons, G W; Pope, C N
2008-01-01
We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor T μν (g αβ , ∂ τ g αβ , ∂ τ ∂ σ g αβ , ...,) constructed from sums of terms, the involving contractions of the metric and powers of arbitrary covariant derivatives of the curvature tensor. A classical solution, such as an Einstein metric, is called universal if, when evaluated on that Einstein metric, T μν is a multiple of the metric. A Ricci flat classical solution is called strongly universal if, when evaluated on that Ricci flat metric, T μν vanishes. It is well known that pp-waves in four spacetime dimensions are strongly universal. We focus attention on a natural generalization; Einstein metrics with holonomy Sim(n - 2) in which all scalar invariants are zero or constant. In four dimensions we demonstrate that the generalized Ghanam-Thompson metric is weakly universal and that the Goldberg-Kerr metric is strongly universal; indeed, we show that universality extends to all four-dimensional Sim(2) Einstein metrics. We also discuss generalizations to higher dimensions
Secure quantum key distribution using squeezed states
International Nuclear Information System (INIS)
Gottesman, Daniel; Preskill, John
2001-01-01
We prove the security of a quantum key distribution scheme based on transmission of squeezed quantum states of a harmonic oscillator. Our proof employs quantum error-correcting codes that encode a finite-dimensional quantum system in the infinite-dimensional Hilbert space of an oscillator, and protect against errors that shift the canonical variables p and q. If the noise in the quantum channel is weak, squeezing signal states by 2.51 dB (a squeeze factor e r =1.34) is sufficient in principle to ensure the security of a protocol that is suitably enhanced by classical error correction and privacy amplification. Secure key distribution can be achieved over distances comparable to the attenuation length of the quantum channel
Allen, Robert C; John, Mallory G; Rutan, Sarah C; Filgueira, Marcelo R; Carr, Peter W
2012-09-07
A singular value decomposition-based background correction (SVD-BC) technique is proposed for the reduction of background contributions in online comprehensive two-dimensional liquid chromatography (LC×LC) data. The SVD-BC technique was compared to simply subtracting a blank chromatogram from a sample chromatogram and to a previously reported background correction technique for one dimensional chromatography, which uses an asymmetric weighted least squares (AWLS) approach. AWLS was the only background correction technique to completely remove the background artifacts from the samples as evaluated by visual inspection. However, the SVD-BC technique greatly reduced or eliminated the background artifacts as well and preserved the peak intensity better than AWLS. The loss in peak intensity by AWLS resulted in lower peak counts at the detection thresholds established using standards samples. However, the SVD-BC technique was found to introduce noise which led to detection of false peaks at the lower detection thresholds. As a result, the AWLS technique gave more precise peak counts than the SVD-BC technique, particularly at the lower detection thresholds. While the AWLS technique resulted in more consistent percent residual standard deviation values, a statistical improvement in peak quantification after background correction was not found regardless of the background correction technique used. Copyright © 2012 Elsevier B.V. All rights reserved.
Superintegrability on the two dimensional hyperboloid
International Nuclear Information System (INIS)
Akopyan, E.; Pogosyan, G.S.; Kalnins, E.G.; Miller, W. Jr
1998-01-01
This work is devoted to the investigation of the quantum mechanical systems on the two dimensional hyperboloid which admit separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of C.P.Boyer, E.G.Kalnins and P.Winternitz, which haven't been studied yet. An example of an interbasis expansion is given and the structure of the quadratic algebra generated by the integrals of motion is carried out
Exact evaluation of entropic quantities in a solvable two-particle model
International Nuclear Information System (INIS)
Glasser, M.L.; Nagy, I.
2013-01-01
It has long been known that the von Neumann entropy S N and the Jozsa–Robb–Wootters subentropy Q JRW [R. Jozsa, et al., Phys. Rev. A 49 (1994) 668] are, respectively, upper and lower bounds on the accessible information one can obtain about the identity of a pure state by performing a quantum measurement on a system whose pure state is initially unknown. We determine these bounds exactly in terms of the occupation numbers of normalized natural orbitals of an externally confined interacting two-particle model system. The occupation numbers are obtained via a sign-correct direct decomposition of the underlying exact Schrödinger wave function in terms of an infinite sum of products of Löwdin's natural orbitals, avoiding thus the solution of the eigenvalue problem with the corresponding reduced one-particle matrix.
Exact evaluation of entropic quantities in a solvable two-particle model
Energy Technology Data Exchange (ETDEWEB)
Glasser, M.L., E-mail: laryg@clarkson.edu [Department of Physics, Clarkson University, Potsdam, NY 13699-5820 (United States); Donostia International Physics Center, P. Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Nagy, I. [Donostia International Physics Center, P. Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1521 Budapest (Hungary)
2013-11-08
It has long been known that the von Neumann entropy S{sub N} and the Jozsa–Robb–Wootters subentropy Q{sub JRW} [R. Jozsa, et al., Phys. Rev. A 49 (1994) 668] are, respectively, upper and lower bounds on the accessible information one can obtain about the identity of a pure state by performing a quantum measurement on a system whose pure state is initially unknown. We determine these bounds exactly in terms of the occupation numbers of normalized natural orbitals of an externally confined interacting two-particle model system. The occupation numbers are obtained via a sign-correct direct decomposition of the underlying exact Schrödinger wave function in terms of an infinite sum of products of Löwdin's natural orbitals, avoiding thus the solution of the eigenvalue problem with the corresponding reduced one-particle matrix.
An Angular Leakage Correction for Modeling a Hemisphere, Using One-Dimensional Spherical Coordinates
International Nuclear Information System (INIS)
Schwinkendorf, K.N.; Eberle, C.S.
2003-01-01
A radially dependent, angular leakage correction was applied to a one-dimensional, multigroup neutron diffusion theory computer code to accurately model hemispherical geometry. This method allows the analyst to model hemispherical geometry, important in nuclear criticality safety analyses, with one-dimensional computer codes, which execute very quickly. Rapid turnaround times for scoping studies thus may be realized. This method uses an approach analogous to an axial leakage correction in a one-dimensional cylinder calculation. The two-dimensional Laplace operator was preserved in spherical geometry using a leakage correction proportional to 1/r 2 , which was folded into the one-dimensional spherical calculation on a mesh-by-mesh basis. Hemispherical geometry is of interest to criticality safety because of its similarity to piles of spilled fissile material and accumulations of fissile material in process containers. A hemisphere also provides a more realistic calculational model for spilled fissile material than does a sphere
Shamim, Saquib; Mahapatra, S; Scappucci, G; Klesse, W M; Simmons, M Y; Ghosh, Arindam
2017-05-04
We report quantum transport measurements on two dimensional (2D) Si:P and Ge:P δ-layers and compare the inelastic scattering rates relevant for weak localization (WL) and universal conductance fluctuations (UCF) for devices of various doping densities (0.3-2.5 × 10 18 m -2 ) at low temperatures (0.3-4.2 K). The phase breaking rate extracted experimentally from measurements of WL correction to conductivity and UCF agree well with each other within the entire temperature range. This establishes that WL and UCF, being the outcome of quantum interference phenomena, are governed by the same dephasing rate.
Chou, Chia-Chun; Kouri, Donald J
2013-04-25
We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.
International Nuclear Information System (INIS)
Frishman, Y.; Zakrewski, W.J.
1989-07-01
We derive explicit expressions for the masses and the binding energies of k-baryons states in two dimensional (one space and one time) Quantum Chromodynamics (QCD(2)). The expressions are given using the parameters n 1 ,n 2 ,...,nN f -1 which characterize the representation of SU(N f ), where N f is the number of flavours, in terms of its Young tableau description. We find that the difference between the mass of the k-baryon state and the sum of masses of any combination of its constituents, is independent of the value N f (ie the number of flavors). These results hold within a certain bosonized form of QCD(2) and within the strong coupling limit of (G/m) → ∞, where G is the gauge coupling constant and m the quark mass. (authors)
One-way quantum computation with four-dimensional photonic qudits
International Nuclear Information System (INIS)
Joo, Jaewoo; Knight, Peter L.; O'Brien, Jeremy L.; Rudolph, Terry
2007-01-01
We consider the possibility of performing linear optical quantum computations making use of extra photonic degrees of freedom. In particular, we focus on the case where we use photons as quadbits, four-dimensional photonic qudits. The basic 2-quadbit cluster state is a hyperentangled state across polarization and two spatial mode degrees of freedom. We examine the nondeterministic methods whereby such states can be created from single photons and/or Bell pairs and then give some mechanisms for performing higher-dimensional fusion gates
On the Convergence in Effective Loop Quantum Cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose Antonio
2010-01-01
In Loop Quantum Cosmology (LQC) there is a discreteness parameter λ, that has been heuristically associated to a fundamental granularity of quantum geometry. It is also possible to consider λ as a regulator in the same spirit as that used in lattice field theory, where it specifies a regular lattice in the real line. A particular quantization of the k = 0 FLRW loop cosmological model yields a completely solvable model, known as solvable loop quantum cosmology(sLQC). In this contribution, we consider effective classical theories motivated by sLQC and study their λ-dependence, with a special interest on the limit λ→0 and the role of the evolution parameter in the convergence of such limit.
Neural network decoder for quantum error correcting codes
Krastanov, Stefan; Jiang, Liang
Artificial neural networks form a family of extremely powerful - albeit still poorly understood - tools used in anything from image and sound recognition through text generation to, in our case, decoding. We present a straightforward Recurrent Neural Network architecture capable of deducing the correcting procedure for a quantum error-correcting code from a set of repeated stabilizer measurements. We discuss the fault-tolerance of our scheme and the cost of training the neural network for a system of a realistic size. Such decoders are especially interesting when applied to codes, like the quantum LDPC codes, that lack known efficient decoding schemes.
Iterative optimization of quantum error correcting codes
International Nuclear Information System (INIS)
Reimpell, M.; Werner, R.F.
2005-01-01
We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds codes outside the usual Knill-Laflamme definition of error correcting codes. The iteration is shown to improve the figure of merit 'channel fidelity' in every step
On the labeling and symmetry adaptation of the solvable finite groups representations
International Nuclear Information System (INIS)
Caride, A.O.; Zanette, S.I.; Nogueira, S.R.A.
1987-01-01
We propose a method to simultaneously perform a symmetry adaptation and a labeling of the bases of the irreducible representations of the solvable finite groups. It is performed by difining a self-adjoint operator with ligenvalues which evidence the descent in symmetry of the group-subgroups sequences. We also prove two theorems on the canonicity of the cpomposition series of the solvable groups. (author) [pt
The Quantum Socket: Wiring for Superconducting Qubits - Part 1
McConkey, T. G.; Bejanin, J. H.; Rinehart, J. R.; Bateman, J. D.; Earnest, C. T.; McRae, C. H.; Rohanizadegan, Y.; Shiri, D.; Mariantoni, M.; Penava, B.; Breul, P.; Royak, S.; Zapatka, M.; Fowler, A. G.
Quantum systems with ten superconducting quantum bits (qubits) have been realized, making it possible to show basic quantum error correction (QEC) algorithms. However, a truly scalable architecture has not been developed yet. QEC requires a two-dimensional array of qubits, restricting any interconnection to external classical systems to the third axis. In this talk, we introduce an interconnect solution for solid-state qubits: The quantum socket. The quantum socket employs three-dimensional wires and makes it possible to connect classical electronics with quantum circuits more densely and accurately than methods based on wire bonding. The three-dimensional wires are based on spring-loaded pins engineered to insure compatibility with quantum computing applications. Extensive design work and machining was required, with focus on material quality to prevent magnetic impurities. Microwave simulations were undertaken to optimize the design, focusing on the interface between the micro-connector and an on-chip coplanar waveguide pad. Simulations revealed good performance from DC to 10 GHz and were later confirmed against experimental measurements.
One-dimensional versus two-dimensional electronic states in vicinal surfaces
International Nuclear Information System (INIS)
Ortega, J E; Ruiz-Oses, M; Cordon, J; Mugarza, A; Kuntze, J; Schiller, F
2005-01-01
Vicinal surfaces with periodic arrays of steps are among the simplest lateral nanostructures. In particular, noble metal surfaces vicinal to the (1 1 1) plane are excellent test systems to explore the basic electronic properties in one-dimensional superlattices by means of angular photoemission. These surfaces are characterized by strong emissions from free-electron-like surface states that scatter at step edges. Thereby, the two-dimensional surface state displays superlattice band folding and, depending on the step lattice constant d, it splits into one-dimensional quantum well levels. Here we use high-resolution, angle-resolved photoemission to analyse surface states in a variety of samples, in trying to illustrate the changes in surface state bands as a function of d
Level crossings in complex two-dimensional potentials
Indian Academy of Sciences (India)
Two-dimensional P T -symmetric quantum-mechanical systems with the complex cubic potential 12 = 2 + 2 + 2 and the complex Hénon–Heiles potential HH = 2 + 2 + (2 − 3/3) are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both ...
Quantum phase transitions in matrix product states of one-dimensional spin-1 chains
International Nuclear Information System (INIS)
Zhu Jingmin
2014-01-01
We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement. (author)
International Nuclear Information System (INIS)
Filgueiras, Cleverson; Rojas, Moises; Aciole, Gilson; Silva, Edilberto O.
2016-01-01
Highlights: • We derive the Schrödinger equation for an electron around a screw dislocation in the presence of an external magnetic field. • We consider the electron confined on an interface. • Modifications due to the screw dislocation on the light interband absorption coefficient and absorption threshold frequency. - Abstract: We investigate the influence of a screw dislocation on the energy levels and the wavefunctions of an electron confined in a two-dimensional pseudoharmonic quantum dot under the influence of an external magnetic field inside a dot and Aharonov–Bohm field inside a pseudodot. The exact solutions for energy eigenvalues and wavefunctions are computed as functions of applied uniform magnetic field strength, Aharonov–Bohm flux, magnetic quantum number and the parameter characterizing the screw dislocation, the Burgers vector. We investigate the modifications due to the screw dislocation on the light interband absorption coefficient and absorption threshold frequency. Two scenarios are possible, depending on if singular effects either manifest or not. We found that as the Burgers vector increases, the curves of frequency are pushed up towards of the growth of it. One interesting aspect which we have observed is that the Aharonov–Bohm flux can be tuned in order to cancel the screw effect of the model.
Energy Technology Data Exchange (ETDEWEB)
Filgueiras, Cleverson, E-mail: cleverson.filgueiras@dfi.ufla.br [Departamento de Física, Universidade Federal de Lavras, Caixa Postal 3037, 37200-000, Lavras, MG (Brazil); Rojas, Moises, E-mail: moises.leyva@dfi.ufla.br [Departamento de Física, Universidade Federal de Lavras, Caixa Postal 3037, 37200-000, Lavras, MG (Brazil); Aciole, Gilson [Unidade Acadêmica de Física, Universidade Federal de Campina Grande, POB 10071, 58109-970, Campina Grande, PB (Brazil); Silva, Edilberto O., E-mail: edilberto.silva@ufma.br [Departamento de Física, Universidade Federal do Maranhão, 65085-580, São Luís, MA (Brazil)
2016-11-25
Highlights: • We derive the Schrödinger equation for an electron around a screw dislocation in the presence of an external magnetic field. • We consider the electron confined on an interface. • Modifications due to the screw dislocation on the light interband absorption coefficient and absorption threshold frequency. - Abstract: We investigate the influence of a screw dislocation on the energy levels and the wavefunctions of an electron confined in a two-dimensional pseudoharmonic quantum dot under the influence of an external magnetic field inside a dot and Aharonov–Bohm field inside a pseudodot. The exact solutions for energy eigenvalues and wavefunctions are computed as functions of applied uniform magnetic field strength, Aharonov–Bohm flux, magnetic quantum number and the parameter characterizing the screw dislocation, the Burgers vector. We investigate the modifications due to the screw dislocation on the light interband absorption coefficient and absorption threshold frequency. Two scenarios are possible, depending on if singular effects either manifest or not. We found that as the Burgers vector increases, the curves of frequency are pushed up towards of the growth of it. One interesting aspect which we have observed is that the Aharonov–Bohm flux can be tuned in order to cancel the screw effect of the model.
Coupled Langmuir oscillations in 2-dimensional quantum plasmas
International Nuclear Information System (INIS)
Akbari-Moghanjoughi, M.
2014-01-01
In this work, we present a hydrodynamic model to study the coupled quantum electron plasma oscillations (QEPO) for two dimensional (2D) degenerate plasmas, which incorporates all the essential quantum ingredients such as the statistical degeneracy pressure, electron-exchange, and electron quantum diffraction effect. Effects of diverse physical aspects like the electronic band-dispersion effect, the electron exchange-correlations and the quantum Bohm-potential as well as other important plasma parameters such as the coupling parameter (plasma separation) and the plasma electron number-densities on the linear response of the coupled system are investigated. By studying three different 2D plasma coupling types, namely, graphene-graphene, graphene-metalfilm, and metalfilm-metalfilm coupling configurations, it is remarked that the collective quantum effects can influence the coupled modes quite differently, depending on the type of the plasma configuration. It is also found that the slow and fast QEPO frequency modes respond very differently to the change in plasma parameters. Current findings can help in understanding of the coupled density oscillations in multilayer graphene, graphene-based heterojunctions, or nanofabricated integrated circuits
Quantum oscillator on CPn in a constant magnetic field
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen
2004-01-01
We construct the quantum oscillator interacting with a constant magnetic field on complex projective spaces CP N , as well as on their noncompact counterparts, i.e., the N-dimensional Lobachewski spaces L N . We find the spectrum of this system and the complete basis of wave functions. Surprisingly, the inclusion of a magnetic field does not yield any qualitative change in the energy spectrum. For N>1 the magnetic field does not break the superintegrability of the system, whereas for N=1 it preserves the exact solvability of the system. We extend these results to the cones constructed over CP N and L N , and perform the Kustaanheimo-Stiefel transformation of these systems to the three dimensional Coulomb-like systems
Universal quantum computation in a semiconductor quantum wire network
International Nuclear Information System (INIS)
Sau, Jay D.; Das Sarma, S.; Tewari, Sumanta
2010-01-01
Universal quantum computation (UQC) using Majorana fermions on a two-dimensional topological superconducting (TS) medium remains an outstanding open problem. This is because the quantum gate set that can be generated by braiding of the Majorana fermions does not include any two-qubit gate and also no single-qubit π/8 phase gate. In principle, it is possible to create these crucial extra gates using quantum interference of Majorana fermion currents. However, it is not clear if the motion of the various order parameter defects (vortices, domain walls, etc.), to which the Majorana fermions are bound in a TS medium, can be quantum coherent. We show that these obstacles can be overcome using a semiconductor quantum wire network in the vicinity of an s-wave superconductor, by constructing topologically protected two-qubit gates and any arbitrary single-qubit phase gate in a topologically unprotected manner, which can be error corrected using magic-state distillation. Thus our strategy, using a judicious combination of topologically protected and unprotected gate operations, realizes UQC on a quantum wire network with a remarkably high error threshold of 0.14 as compared to 10 -3 to 10 -4 in ordinary unprotected quantum computation.
Ising critical behaviour in the one-dimensional frustrated quantum XY model
International Nuclear Information System (INIS)
Granato, E.
1993-06-01
A generalization of the one-dimensional frustrated quantum XY model is considered in which the inter and intra-chain coupling constants of the two infinite XY (planar rotor) chains have different strengths. The model can describe the superconductor-insulator transition due to charging effects in a ladder of Josephson junctions in a magnetic field with half a flux quantum per plaquette. From a fluctuation-effective action, this transition is expected to be in the universality class of the two-dimensional classical XY-Ising model. The critical behaviour is studied using a Monte Carlo transfer matrix applied to the path-integral representation of the model and a finite-size-scaling analysis of data on small system sizes. It is found that, unlike the previous studied case of equal inter and intra-chain coupling constants, the XY and Ising-like excitations of the quantum model decouple for large interchain coupling, giving rise to pure Ising model critical behaviour for the chirality order parameter in good agreement with the results for the XY-Ising model. (author). 18 refs, 4 figs
A New Class of Solvable Many-Body Problems
Directory of Open Access Journals (Sweden)
Francesco Calogero
2012-10-01
Full Text Available A new class of solvable N-body problems is identified. They describe N unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion ''of goldfish type'' (acceleration equal force, with specific velocity-dependent one-body and two-body forces featuring several arbitrary coupling constants. The corresponding initial-value problems are solved by finding the eigenvalues of a time-dependent N×N matrix U(t explicitly defined in terms of the initial positions and velocities of the N particles. Some of these models are asymptotically isochronous, i.e. in the remote future they become completely periodic with a period T independent of the initial data (up to exponentially vanishing corrections. Alternative formulations of these models, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited.
Exact solutions of the vacuum Einstein's equations allowing for two noncommuting Killing vectors
International Nuclear Information System (INIS)
Aliev, V.N.; Leznov, A.N.
1990-01-01
Einstein's equations are written in the form of covariant gauge theory in two-dimensional space with binomial solvable gauge group, with respect to two noncommutative of Killing vectors. The theory is exact integrable in one-dimensional case and series of partial exact solutions are constructed in two-dimensional. 5 refs
Paston, S A; Prokhvatilov, E V
2002-01-01
The Hamiltonian, reproducing the results of the two-dimensional quantum electrodynamics in the Lorentz coordinates, is constructed on the light front. The procedure of bosonization and analysis of the boson perturbation theory in all the orders by the fermions mass are applied for this purpose. Besides the common terms, originating by the naive quantization on the light front, the obtained Hamiltonian contains an additional counterterm. It is proportional to the linear combination of the fermion zero modes (multiplied by a certain factor compensating the charge and fermion number). The coefficient before this counterterm has no ultraviolet divergence, depends on the value of the fermion condensate in the theta-vacuum and by the small fermion mass is linear by it
Novais, E.; Mucciolo, Eduardo R.; Baranger, Harold U.
2008-07-01
We analyze the long-time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is indeed possible, we find formal expressions for the probability of a given syndrome history and the associated residual decoherence encoded in the reduced density matrix. Systems with nonzero gate times (“long gates”) are included in our analysis by using an upper bound on the noise. In order to introduce the local error probability for a qubit, we assume that propagation of signals through the environment is slower than the QEC period (hypercube assumption). This allows an explicit calculation in the case of a generalized spin-boson model and a quantum frustration model. The key result is a dimensional criterion: If the correlations decay sufficiently fast, the system evolves toward a stochastic error model for which the threshold theorem of fault-tolerant quantum computation has been proven. On the other hand, if the correlations decay slowly, the traditional proof of this threshold theorem does not hold. This dimensional criterion bears many similarities to criteria that occur in the theory of quantum phase transitions.
Infinite dimensional groups and algebras in quantum physics
International Nuclear Information System (INIS)
Ottesen, J.T.
1995-01-01
This book is an introduction to the application of infite-dimensional groups and algebras in quantum physics. Especially considered are the spin representation of the infinite-dimensional orthogonal group, the metaplectic representation of the infinite-dimensional symplectic groups, and Loop and Virasoro algebras. (HSI)
Marinescu, D. C.
2017-09-01
We evaluate the quantum corrections to the conductivity of a two-dimensional electron system with competing Rashba (R) and linear and cubic Dresselhaus (D) spin-orbit interactions in the presence of an in-plane magnetic field B . Within a perturbative approximation, we investigate the interplay between the spin-orbit coupling and the magnetic field in determining the transport regime in two different limiting scenarios: when only one of the linear terms, either Rashba or Dresselhaus, dominates, and at equal linear couplings, when the cubic Dresselhaus breaks the spin symmetry. In each instance, we find that for B higher than a critical value, the antilocalization correction is suppressed and the effective dephasing time saturates to a constant value determined only by the spin-orbit interaction. At equal R-D linear couplings, this value is directly proportional with the cubic Dresselhaus contribution. In the same regime, the magnetoconductivity is expressed as a simple logarithmic function dependent only on the cubic Dresselhaus constant.
Two solvable problems of planar geometrical optics.
Borghero, Francesco; Bozis, George
2006-12-01
In the framework of geometrical optics we consider a two-dimensional transparent inhomogeneous isotropic medium (dispersive or not). We show that (i) for any family belonging to a certain class of planar monoparametric families of monochromatic light rays given in the form f(x,y)=c of any definite color and satisfying a differential condition, all the refractive index profiles n=n(x,y) allowing for the creation of the given family can be found analytically (inverse problem) and that (ii) for any member of a class of two-dimensional refractive index profiles n=n(x,y) satisfying a differential condition, all the compatible families of light rays can be found analytically (direct problem). We present appropriate examples.
Quantum states and their marginals. From multipartite entanglement to quantum error-correcting codes
International Nuclear Information System (INIS)
Huber, Felix Michael
2017-01-01
At the heart of the curious phenomenon of quantum entanglement lies the relation between the whole and its parts. In my thesis, I explore different aspects of this theme in the multipartite setting by drawing connections to concepts from statistics, graph theory, and quantum error-correcting codes: first, I address the case when joint quantum states are determined by their few-body parts and by Jaynes' maximum entropy principle. This can be seen as an extension of the notion of entanglement, with less complex states already being determined by their few-body marginals. Second, I address the conditions for certain highly entangled multipartite states to exist. In particular, I present the solution of a long-standing open problem concerning the existence of an absolutely maximally entangled state on seven qubits. This sheds light on the algebraic properties of pure quantum states, and on the conditions that constrain the sharing of entanglement amongst multiple particles. Third, I investigate Ulam's graph reconstruction problems in the quantum setting, and obtain legitimacy conditions of a set of states to be the reductions of a joint graph state. Lastly, I apply and extend the weight enumerator machinery from quantum error correction to investigate the existence of codes and highly entangled states in higher dimensions. This clarifies the physical interpretation of the weight enumerators and of the quantum MacWilliams identity, leading to novel applications in multipartite entanglement.
Generation of acoustic phonons from quasi-two-dimensional hole gas
International Nuclear Information System (INIS)
Singh, J.; Oh, I.K.
2002-01-01
Full text: Generation of phonons from two dimensional electron and hole gases in quantum wells has attracted much attraction recently. The mechanism of phonon emission plays an important role in the phonon spectroscopy which enables us to study the angular and polarization dependence of phonon emission. The acoustic phonon emission from a quasi-two-dimensional hole gas (2DHG) in quantum wells is influenced by the anisotropic factors in the valence band structure, screening, elastic property, etc. The anisotropy in the valence band structure gives rise to anisotropic effective mass and deformation potential and that in the elastic constants leads to anisotropic sound velocity. Piezoelectric coupling in non-centrosymmetric materials such as GaAs is also anisotropic. In this paper, considering the anisotropy in the effective mass, deformation potential, piezoelectric coupling and screening effect, we present a theory to study the angular and polarization dependence of acoustic phonon emission from a quasi-2DHG in quantum wells. The theory is finally applied to calculate the rate of acoustic phonon emission in GaAs quantum wells
Quantum-electrodynamics corrections in pionic hydrogen
Schlesser, S.; Le Bigot, E. -O.; Indelicato, P.; Pachucki, K.
2011-01-01
We investigate all pure quantum-electrodynamics corrections to the np --> 1s, n = 2-4 transition energies of pionic hydrogen larger than 1 meV, which requires an accurate evaluation of all relevant contributions up to order alpha 5. These values are needed to extract an accurate strong interaction
Two-loop corrections for nuclear matter in the Walecka model
International Nuclear Information System (INIS)
Furnstahl, R.J.; Perry, R.J.; Serot, B.D.; Department of Physics, The Ohio State University, Columbus, Ohio 43210; Physics Department and Nuclear Theory Center, Indiana University, Bloomington, Indiana 47405)
1989-01-01
Two-loop corrections for nuclear matter, including vacuum polarization, are calculated in the Walecka model to study the loop expansion as an approximation scheme for quantum hadrodynamics. Criteria for useful approximation schemes are discussed, and the concepts of strong and weak convergence are introduced. The two-loop corrections are evaluated first with one-loop parameters and mean fields and then by minimizing the total energy density with respect to the scalar field and refitting parameters to empirical nuclear matter saturation properties. The size and nature of the corrections indicate that the loop expansion is not convergent at two-loop order in either the strong or weak sense. Prospects for alternative approximation schemes are discussed
Automated Processing of Two-Dimensional Correlation Spectra
Sengstschmid; Sterk; Freeman
1998-04-01
An automated scheme is described which locates the centers of cross peaks in two-dimensional correlation spectra, even under conditions of severe overlap. Double-quantum-filtered correlation (DQ-COSY) spectra have been investigated, but the method is also applicable to TOCSY and NOESY spectra. The search criterion is the intrinsic symmetry (or antisymmetry) of cross-peak multiplets. An initial global search provides the preliminary information to build up a two-dimensional "chemical shift grid." All genuine cross peaks must be centered at intersections of this grid, a fact that reduces the extent of the subsequent search program enormously. The program recognizes cross peaks by examining the symmetry of signals in a test zone centered at a grid intersection. This "symmetry filter" employs a "lowest value algorithm" to discriminate against overlapping responses from adjacent multiplets. A progressive multiplet subtraction scheme provides further suppression of overlap effects. The processed two-dimensional correlation spectrum represents cross peaks as points at the chemical shift coordinates, with some indication of their relative intensities. Alternatively, the information is presented in the form of a correlation table. The authenticity of a given cross peak is judged by a set of "confidence criteria" expressed as numerical parameters. Experimental results are presented for the 400-MHz double-quantum-filtered COSY spectrum of 4-androsten-3,17-dione, a case where there is severe overlap. Copyright 1998 Academic Press.
International Nuclear Information System (INIS)
Endo, Takako; Konno, Norio; Obuse, Hideaki; Segawa, Etsuo
2017-01-01
In this paper, we treat quantum walks in a two-dimensional lattice with cutting edges along a straight boundary introduced by Asboth and Edge (2015 Phys. Rev . A 91 022324) in order to study one-dimensional edge states originating from topological phases of matter and to obtain collateral evidence of how a quantum walker reacts to the boundary. Firstly, we connect this model to the CMV matrix, which provides a 5-term recursion relation of the Laurent polynomial associated with spectral measure on the unit circle. Secondly, we explicitly derive the spectra of bulk and edge states of the quantum walk with the boundary using spectral analysis of the CMV matrix. Thirdly, while topological numbers of the model studied so far are well-defined only when gaps in the bulk spectrum exist, we find a new topological number defined only when there are no gaps in the bulk spectrum. We confirm that the existence of the spectrum for edge states derived from the CMV matrix is consistent with the prediction from a bulk-edge correspondence using topological numbers calculated in the cases where gaps in the bulk spectrum do or do not exist. Finally, we show how the edge states contribute to the asymptotic behavior of the quantum walk through limit theorems of the finding probability. Conversely, we also propose a differential equation using this limit distribution whose solution is the underlying edge state. (paper)
International Nuclear Information System (INIS)
Gvozdikov, V M; Taut, M
2009-01-01
We report on analytical and numerical studies of the magnetic quantum oscillations of the diagonal conductivity σ xx in a two-dimensional conductor with a weak square superlattice modulation under conditions of the integer quantum Hall (IQHE) effect. The quantum Hall effect in such a system differs from the conventional IQHE, in which the finite width of the Landau bands is due to disorder only. The superlattice modulation potential yields a fractal splitting of the Landau levels into Hofstadter minibands. For rational flux through a unit cell, the minibands have a finite width and intrinsic dispersion relations. We consider a regime, now accessible experimentally, in which disorder does not wash out the fractal internal gap structure of the Landau bands completely. We found the following distinctions from the conventional IQHE produced by the superlattice: (i) the peaks in diagonal conductivity are split due to the Hofstadter miniband structure of Landau bands; (ii) the number of split peaks in the bunch, their positions and heights depend irregularly on the magnetic field and the Fermi energy; (iii) the gaps between the split Landau bands (and related quantum Hall plateaus) become narrower with the superlattice modulation than without it.
Huo, Ming-Xia; Li, Ying
2017-12-01
Quantum error correction is important to quantum information processing, which allows us to reliably process information encoded in quantum error correction codes. Efficient quantum error correction benefits from the knowledge of error rates. We propose a protocol for monitoring error rates in real time without interrupting the quantum error correction. Any adaptation of the quantum error correction code or its implementation circuit is not required. The protocol can be directly applied to the most advanced quantum error correction techniques, e.g. surface code. A Gaussian processes algorithm is used to estimate and predict error rates based on error correction data in the past. We find that using these estimated error rates, the probability of error correction failures can be significantly reduced by a factor increasing with the code distance.
Workshop on low-dimensional quantum field theory and its applications
International Nuclear Information System (INIS)
Yamamoto, Hisashi
1990-02-01
The workshop on 'Low-Dimensional Quantum Field Theory and its Applications' was held at INS on December 18 - 20, 1989 with about seventy participants. Some pedagogical reviews and the latest results were delivered on the recent topics related to both solid-state and particle physics. Among them are quantum Hall effect, high T c superconductivity and related topics in low-dimensional quantum field theory. Many active discussions were made on these issues. (J.P.N.)
Solvability conditions for dendritic growth in the boundary-layer model with capillary anisotropy
Langer, J. S.; Hong, D. C.
1986-01-01
This paper is concerned primarily with the development of an analytic approach to the theory of steady-state velocity selection in the boundary-layer model of dendritic solidification. The two-dimensional version of this model with a fourfold crystalline anisotropy alpha in the surface tension is considered. By extending a WKB method introduced in an earlier paper, the alpha dependence of the selected growth rate is determined in the limit of small alpha; and this rate is studied for large alphas in the limit in which the dimensionless undercooling approaches unity. Portions of the paper are devoted to a reinterpretation of the mathematical structure of the solvability condition in problems of this kind.
Comparative analysis of peak-detection techniques for comprehensive two-dimensional chromatography.
Latha, Indu; Reichenbach, Stephen E; Tao, Qingping
2011-09-23
Comprehensive two-dimensional gas chromatography (GC×GC) is a powerful technology for separating complex samples. The typical goal of GC×GC peak detection is to aggregate data points of analyte peaks based on their retention times and intensities. Two techniques commonly used for two-dimensional peak detection are the two-step algorithm and the watershed algorithm. A recent study [4] compared the performance of the two-step and watershed algorithms for GC×GC data with retention-time shifts in the second-column separations. In that analysis, the peak retention-time shifts were corrected while applying the two-step algorithm but the watershed algorithm was applied without shift correction. The results indicated that the watershed algorithm has a higher probability of erroneously splitting a single two-dimensional peak than the two-step approach. This paper reconsiders the analysis by comparing peak-detection performance for resolved peaks after correcting retention-time shifts for both the two-step and watershed algorithms. Simulations with wide-ranging conditions indicate that when shift correction is employed with both algorithms, the watershed algorithm detects resolved peaks with greater accuracy than the two-step method. Copyright © 2011 Elsevier B.V. All rights reserved.
Quantum Fluctuations of Low Dimensional Bose-Einstein ...
African Journals Online (AJOL)
A system of low dimensional condensed ultracold atomic gases inside a field of a laser-driven optical cavity exhibits dispersive optical bistability. During such a process the system also shows quantum fluctuations. Condensate fluctuations are highly manifested particularly in low dimensional systems. In this paper we have ...
International Nuclear Information System (INIS)
den Hartog, S.G.; van Wees, B.J.; Klapwijk, T.M.; Nazarov, Y.V.; Borghs, G.
1997-01-01
We have investigated the superconducting-phase-modulated reduction in the resistance of a ballistic quantum point contact (QPC) connected via a disordered two-dimensional electron gas (2DEG) to superconductors. We show that this reduction is caused by coherent Andreev backscattering of holes through the QPC, which increases monotonically by reducing the bias voltage to zero. In contrast, the magnitude of the phase-dependent resistance of the disordered 2DEG displays a nonmonotonic reentrant behavior versus bias voltage. copyright 1997 The American Physical Society
Erratum: Quantum corrections and black hole spectroscopy
Jiang, Qing-Quan; Han, Yan; Cai, Xu
2012-06-01
In my paper [Qing-Quan Jiang, Yan Han, Xu Cai, Quantum corrections and black hole spectroscopy, JHEP 08 (2010) 049], there was an error in deriving the black hole spectroscopy. In this erratum, we attempt to rectify them.
Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system
International Nuclear Information System (INIS)
Castelnovo, Claudio; Chamon, Claudio; Mudry, Christopher; Pujol, Pierre
2007-01-01
We construct a local interacting quantum dimer model on the square lattice, whose zero-temperature phase diagram is characterized by a line of critical points separating two ordered phases of the valence bond crystal type. On one side, the line of critical points terminates in a quantum transition inherited from a Kosterlitz-Thouless transition in an associated classical model. We also discuss the effect of a longer-range dimer interaction that can be used to suppress the line of critical points by gradually shrinking it to a single point. Finally, we propose a way to generalize the quantum Hamiltonian to a dilute dimer model in presence of monomers and we qualitatively discuss the phase diagram
Generation and confirmation of a (100 x 100)-dimensional entangled quantum system.
Krenn, Mario; Huber, Marcus; Fickler, Robert; Lapkiewicz, Radek; Ramelow, Sven; Zeilinger, Anton
2014-04-29
Entangled quantum systems have properties that have fundamentally overthrown the classical worldview. Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature, and moreover also enables genuinely new protocols for quantum information processing. Here we present the creation of a (100 × 100)-dimensional entangled quantum system, using spatial modes of photons. For its verification we develop a novel nonlinear criterion which infers entanglement dimensionality of a global state by using only information about its subspace correlations. This allows very practical experimental implementation as well as highly efficient extraction of entanglement dimensionality information. Applications in quantum cryptography and other protocols are very promising.
Generation and confirmation of a (100 × 100)-dimensional entangled quantum system
Krenn, Mario; Huber, Marcus; Fickler, Robert; Lapkiewicz, Radek; Ramelow, Sven; Zeilinger, Anton
2014-01-01
Entangled quantum systems have properties that have fundamentally overthrown the classical worldview. Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature, and moreover also enables genuinely new protocols for quantum information processing. Here we present the creation of a (100 × 100)-dimensional entangled quantum system, using spatial modes of photons. For its verification we develop a novel nonlinear criterion which infers entanglement dimensionality of a global state by using only information about its subspace correlations. This allows very practical experimental implementation as well as highly efficient extraction of entanglement dimensionality information. Applications in quantum cryptography and other protocols are very promising. PMID:24706902
Energy Technology Data Exchange (ETDEWEB)
Goswami, Srijit; Aamir, Mohammed Ali; Shamim, Saquib; Ghosh, Arindam [Department of Physics, Indian Institute of Science, Bangalore 560 012 (India); Siegert, Christoph; Farrer, Ian; Ritchie, David A. [Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Pepper, Michael [Department of Electrical and Electronic Engineering, University College, London WC1E 7JE (United Kingdom)
2013-12-04
We use a dual gated device structure to introduce a gate-tuneable periodic potential in a GaAs/AlGaAs two dimensional electron gas (2DEG). Using only a suitable choice of gate voltages we can controllably alter the potential landscape of the bare 2DEG, inducing either a periodic array of antidots or quantum dots. Antidots are artificial scattering centers, and therefore allow for a study of electron dynamics. In particular, we show that the thermovoltage of an antidot lattice is particularly sensitive to the relative positions of the Fermi level and the antidot potential. A quantum dot lattice, on the other hand, provides the opportunity to study correlated electron physics. We find that its current-voltage characteristics display a voltage threshold, as well as a power law scaling, indicative of collective Coulomb blockade in a disordered background.
International Nuclear Information System (INIS)
Goswami, Srijit; Aamir, Mohammed Ali; Shamim, Saquib; Ghosh, Arindam; Siegert, Christoph; Farrer, Ian; Ritchie, David A.; Pepper, Michael
2013-01-01
We use a dual gated device structure to introduce a gate-tuneable periodic potential in a GaAs/AlGaAs two dimensional electron gas (2DEG). Using only a suitable choice of gate voltages we can controllably alter the potential landscape of the bare 2DEG, inducing either a periodic array of antidots or quantum dots. Antidots are artificial scattering centers, and therefore allow for a study of electron dynamics. In particular, we show that the thermovoltage of an antidot lattice is particularly sensitive to the relative positions of the Fermi level and the antidot potential. A quantum dot lattice, on the other hand, provides the opportunity to study correlated electron physics. We find that its current-voltage characteristics display a voltage threshold, as well as a power law scaling, indicative of collective Coulomb blockade in a disordered background
Continuous quantum error correction for non-Markovian decoherence
International Nuclear Information System (INIS)
Oreshkov, Ognyan; Brun, Todd A.
2007-01-01
We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-correction rates, the encoded state approximately follows an evolution of the type of a single decohering qubit, but with an effectively decreased coupling constant. The factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. The quadratic enhancement depends on the existence of a Zeno regime in the Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze the range of validity of this result and identify two relevant time scales. Finally, we extend the result to more general codes and argue that the performance of continuous error correction will exhibit the same qualitative characteristics
Solving the two-dimensional Schrödinger equation using basis ...
Indian Academy of Sciences (India)
Ihab H Naeim
2017-10-19
Oct 19, 2017 ... We shall study the case of a two-dimensional quantum system .... Solving (6) for ck,l is tantamount to pro- ... case, the final computational problem becomes quite ..... matrix approach fails in the case of two particles con-.
Entanglement in a simple quantum phase transition
International Nuclear Information System (INIS)
Osborne, Tobias J.; Nielsen, Michael A.
2002-01-01
What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice
Quantum Phenomena in Low-Dimensional Systems
Geller, Michael R.
2001-01-01
A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.
International Nuclear Information System (INIS)
Decca, R.S.; Fischbach, E.; Klimchitskaya, G.L.; Mostepanenko, V.M.; Krause, D.E.; Lopez, D.
2003-01-01
We report new constraints on extra-dimensional models and other physics beyond the standard model based on measurements of the Casimir force between two dissimilar metals for separations in the range 0.2-1.2 μm. The Casimir force between a Au-coated sphere and a Cu-coated plate of a microelectromechanical torsional oscillator was measured statically with an absolute error of 0.3 pN. In addition, the Casimir pressure between two parallel plates was determined dynamically with an absolute error of ≅0.6 mPa. Within the limits of experimental and theoretical errors, the results are in agreement with a theory that takes into account the finite conductivity and roughness of the two metals. The level of agreement between experiment and theory was then used to set limits on the predictions of extra-dimensional physics and thermal quantum field theory. It is shown that two theoretical approaches to the thermal Casimir force which predict effects linear in temperature are ruled out by these experiments. Finally, constraints on Yukawa corrections to Newton's law of gravity are strengthened by more than an order of magnitude in the range 56-330 nm
Experiments on two-resonator circuit quantum electrodynamics. A superconducting quantum switch
International Nuclear Information System (INIS)
Hoffmann, Elisabeth Christiane Maria
2013-01-01
The field of cavity quantum electrodynamics (QED) studies the interaction between light and matter on a fundamental level. In typical experiments individual natural atoms are interacting with individual photons trapped in three-dimensional cavities. Within the last decade the prospering new field of circuit QED has been developed. Here, the natural atoms are replaced by artificial solid state quantum circuits offering large dipole moments which are coupled to quasi-onedimensional cavities providing a small mode volume and hence a large vacuum field strength. In our experiments Josephson junction based superconducting quantum bits are coupled to superconducting microwave resonators. In circuit QED the number of parameters that can be varied is increased and regimes that are not accessible using natural atoms can be entered and investigated. Apart from design flexibility and tunability of system parameters a particular advantage of circuit QED is the scalability to larger system size enabled by well developed micro- and nanofabrication tools. When scaling up the resonator-qubit systems beyond a few coupled circuits, the rapidly increasing number of interacting subsystems requires an active control and directed transmission of quantum signals. This can, for example, be achieved by implementing switchable coupling between two microwave resonators. To this end, a superconducting flux qubit is used to realize a suitable coupling between two microwave resonators, all working in the Gigahertz regime. The resulting device is called quantum switch. The flux qubit mediates a second order tunable and switchable coupling between the resonators. Depending on the qubit state, this coupling can compensate for the direct geometric coupling of the two resonators. As the qubit may also be in a quantum superposition state, the switch itself can be ''quantum'': it can be a superposition of ''on'' and ''off''. This work presents the theoretical background, the fabrication techniques and
Two-dimensional Semiconductor-Superconductor Hybrids
DEFF Research Database (Denmark)
Suominen, Henri Juhani
This thesis investigates hybrid two-dimensional semiconductor-superconductor (Sm-S) devices and presents a new material platform exhibiting intimate Sm-S coupling straight out of the box. Starting with the conventional approach, we investigate coupling superconductors to buried quantum well....... To overcome these issues we integrate the superconductor directly into the semiconducting material growth stack, depositing it in-situ in a molecular beam epitaxy system under high vacuum. We present a number of experiments on these hybrid heterostructures, demonstrating near unity interface transparency...
Quantum transport in strongly interacting one-dimensional nanostructures
Agundez, R.R.
2015-01-01
In this thesis we study quantum transport in several one-dimensional systems with strong electronic interactions. The first chapter contains an introduction to the concepts treated throughout this thesis, such as the Aharonov-Bohm effect, the Kondo effect, the Fano effect and quantum state transfer.
Universality of modular symmetries in two-dimensional magnetotransport
Olsen, K. S.; Limseth, H. S.; Lütken, C. A.
2018-01-01
We analyze experimental quantum Hall data from a wide range of different materials, including semiconducting heterojunctions, thin films, surface layers, graphene, mercury telluride, bismuth antimonide, and black phosphorus. The fact that these materials have little in common, except that charge transport is effectively two-dimensional, shows how robust and universal the quantum Hall phenomenon is. The scaling and fixed point data we analyzed appear to show that magnetotransport in two dimensions is governed by a small number of universality classes that are classified by modular symmetries, which are infinite discrete symmetries not previously seen in nature. The Hall plateaux are (infrared) stable fixed points of the scaling-flow, and quantum critical points (where the wave function is delocalized) are unstable fixed points of scaling. Modular symmetries are so rigid that they in some cases fix the global geometry of the scaling flow, and therefore predict the exact location of quantum critical points, as well as the shape of flow lines anywhere in the phase diagram. We show that most available experimental quantum Hall scaling data are in good agreement with these predictions.
Dolan-Grady relations and noncommutative quasi-exactly solvable systems
International Nuclear Information System (INIS)
Klishevich, Sergey M; Plyushchay, Mikhail S
2003-01-01
We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the su(2) and sl(2,R) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems
Laterally coupled jellium-like two-dimensional quantum dots
Markvoort, Albert. J.; Hilbers, P.A.J.; Pino, R.
2003-01-01
Many studies have been performed to describe quantum dots using a parabolic confining potential. However, infinite potentials are unphysical and lead to problems when describing laterally coupled quantum dots. We propose the use of the parabolic potential of a homogeneous density distribution within
Directory of Open Access Journals (Sweden)
T. H. Raupach
2015-01-01
Full Text Available The raindrop size distribution (DSD quantifies the microstructure of rainfall and is critical to studying precipitation processes. We present a method to improve the accuracy of DSD measurements from Parsivel (particle size and velocity disdrometers, using a two-dimensional video disdrometer (2DVD as a reference instrument. Parsivel disdrometers bin raindrops into velocity and equivolume diameter classes, but may misestimate the number of drops per class. In our correction method, drop velocities are corrected with reference to theoretical models of terminal drop velocity. We define a filter for raw disdrometer measurements to remove particles that are unlikely to be plausible raindrops. Drop concentrations are corrected such that on average the Parsivel concentrations match those recorded by a 2DVD. The correction can be trained on and applied to data from both generations of OTT Parsivel disdrometers, and indeed any disdrometer in general. The method was applied to data collected during field campaigns in Mediterranean France for a network of first- and second-generation Parsivel disdrometers, and on a first-generation Parsivel in Payerne, Switzerland. We compared the moments of the resulting DSDs to those of a collocated 2DVD, and the resulting DSD-derived rain rates to collocated rain gauges. The correction improved the accuracy of the moments of the Parsivel DSDs, and in the majority of cases the rain rate match with collocated rain gauges was improved. In addition, the correction was shown to be similar for two different climatologies, suggesting its general applicability.
Viswanathan, T M; Viswanathan, G M
2011-01-28
Strong global solvability is difficult to prove for high-dimensional hydrodynamic systems because of the complex interplay between nonlinearity and scale invariance. We define the Ladyzhenskaya-Lions exponent α(L)(n)=(2+n)/4 for Navier-Stokes equations with dissipation -(-Δ)(α) in R(n), for all n≥2. We review the proof of strong global solvability when α≥α(L)(n), given smooth initial data. If the corresponding Euler equations for n>2 were to allow uncontrolled growth of the enstrophy (1/2)∥∇u∥(L²)(2), then no globally controlled coercive quantity is currently known to exist that can regularize solutions of the Navier-Stokes equations for α<α(L)(n). The energy is critical under scale transformations only for α=α(L)(n).
Integrable Time-Dependent Quantum Hamiltonians
Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen
2018-05-01
We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.
Superintegrability in two-dimensional Euclidean space and associated polynomial solutions
International Nuclear Information System (INIS)
Kalnins, E.G.; Miller, W. Jr; Pogosyan, G.S.
1996-01-01
In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the spectral functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial base for each of the nonsubgroup base, not just the subgroup cartesian and polar coordinate case, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the N-dimensional isotropic quantum oscillator. 28 refs., 1 tab
Electromagnetic fields with vanishing quantum corrections
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello; Pravda, Vojtěch
2018-01-01
Roč. 779, 10 April (2018), s. 393-395 ISSN 0370-2693 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : nonlinear electrodynamics * quantum corrections Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.807, year: 2016 https://www.sciencedirect.com/science/article/pii/S0370269318300327?via%3Dihub
Electromagnetic fields with vanishing quantum corrections
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello; Pravda, Vojtěch
2018-01-01
Roč. 779, 10 April (2018), s. 393-395 ISSN 0370-2693 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : nonlinear electrodynamics * quantum corrections Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.807, year: 2016 https://www. science direct.com/ science /article/pii/S0370269318300327?via%3Dihub
Quantum confinement effects in low-dimensional systems
Indian Academy of Sciences (India)
2015-06-03
Jun 3, 2015 ... Quantum confinement effects in low-dimensional systems. Figure 5. (a) Various cuts of the three-dimensional data showing energy vs. momen- tum dispersion relations for Ag film of 17 ML thickness on Ge(111). (b) Photo- emission intensity maps along ¯M– ¯ – ¯K direction. (c) Substrate bands replotted ...
Anonymous voting for multi-dimensional CV quantum system
International Nuclear Information System (INIS)
Shi Rong-Hua; Xiao Yi; Shi Jin-Jing; Guo Ying; Lee, Moon-Ho
2016-01-01
We investigate the design of anonymous voting protocols, CV-based binary-valued ballot and CV-based multi-valued ballot with continuous variables (CV) in a multi-dimensional quantum cryptosystem to ensure the security of voting procedure and data privacy. The quantum entangled states are employed in the continuous variable quantum system to carry the voting information and assist information transmission, which takes the advantage of the GHZ-like states in terms of improving the utilization of quantum states by decreasing the number of required quantum states. It provides a potential approach to achieve the efficient quantum anonymous voting with high transmission security, especially in large-scale votes. (paper)
Two-dimensional models in statistical mechanics and field theory
International Nuclear Information System (INIS)
Koberle, R.
1980-01-01
Several features of two-dimensional models in statistical mechanics and Field theory, such as, lattice quantum chromodynamics, Z(N), Gross-Neveu and CP N-1 are discussed. The problems of confinement and dynamical mass generation are also analyzed. (L.C.) [pt
Quantum hoop conjecture: Black hole formation by particle collisions
Energy Technology Data Exchange (ETDEWEB)
Casadio, Roberto, E-mail: casadio@bo.infn.it [Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126 Bologna (Italy); I.N.F.N., Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna (Italy); Micu, Octavian, E-mail: octavian.micu@spacescience.ro [Institute of Space Science, Bucharest, P.O. Box MG-23, RO-077125 Bucharest-Magurele (Romania); Scardigli, Fabio, E-mail: fabio@phys.ntu.edu.tw [Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano (Italy); Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2014-05-01
We address the issue of (quantum) black hole formation by particle collision in quantum physics. We start by constructing the horizon wave-function for quantum mechanical states representing two highly boosted non-interacting particles that collide in flat one-dimensional space. From this wave-function, we then derive a probability that the system becomes a black hole as a function of the initial momenta and spatial separation between the particles. This probability allows us to extend the hoop conjecture to quantum mechanics and estimate corrections to its classical counterpart.
Fiore, A.; Rossetti, M.; Alloing, B.; Paranthoën, C.; Chen, J.X.; Geelhaar, L.; Riechert, H.
2004-01-01
We present a comparative study of carrier diffusion in semiconductor heterostructures with different dimensionality [InGaAs quantum wells (QWs), InAs quantum dots (QDs), and disordered InGaNAs QWs (DQWs)]. In order to evaluate the diffusion length in the active region of device structures, we
Scattering theory for self-adjoint extensions
International Nuclear Information System (INIS)
Kuperin, Yu.A.; Pavlov, B.S.; Kurasov, P.B.; Makarov, K.A.; Melnikov, Yu. B.; Yevstratov, V.V
1989-01-01
In this paper a new approach is suggested to the construction of a wide class of exactly solvable quantum-mechanical models of scattering, quantum-mechanical models of solids and an exactly solvable quantum-stochastical model. For most of the models the spectral analysis is performed in an explicit form, for many body problems it is reduced to one-dimensional integral equations. The construction of all models is based on a new version of extension theory, which uses the boundary forms for abstract operators. This version gives a simple and general method to join the pair of operators, one of them abstract, and the other one differential. The solvability of these models is based on Krein's formula for quasiresolvents
Lamb shift of energy levels in quantum rings
International Nuclear Information System (INIS)
Kryuchkyan, G Yu; Kyriienko, O; Shelykh, I A
2015-01-01
We study the vacuum radiative corrections to energy levels of a confined electron in quantum rings. The calculations are provided for the Lamb shift of energy levels in a low-momentum region of virtual photons and for both one-dimensional and two-dimensional quantum rings. We show that contrary to the well known case of a hydrogen atom the value of the Lamb shift increases with the magnetic momentum quantum number m. We also investigate the dependence of the Lamb shift on magnetic flux piercing the ring and demonstrate a presence of magnetic-flux-dependent oscillations. For a one-dimensional ring the value of the shift strongly depends on the radius of the ring. It is small for semiconductor rings but can attain measurable quantities in natural organic ring-shape molecules, such as benzene, cycloalcanes and porphyrins. (paper)
Quantum gravitational corrections to the functional Schroedinger equation
International Nuclear Information System (INIS)
Kiefer, C.; Singh, T.P.
1990-10-01
We derive corrections to the Schroedinger equation which arise from the quantization of the gravitational field. This is achieved through an expansion of the full functional Wheeler-DeWitt equation with respect to powers of the Planck mass. We demonstrate that the corrections terms are independent of the factor ordering which is chosen for the gravitational kinetic term. Although the corrections are numerically extremely tiny, we show how they lead, at least in principle, to shift in the spectral lines of hydrogen type atoms. We discuss the significance of these corrections for quantum field theory near the Planck scale. (author). 35 refs
Error Correction for Non-Abelian Topological Quantum Computation
Directory of Open Access Journals (Sweden)
James R. Wootton
2014-03-01
Full Text Available The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However, the question of how to obtain and process information about what errors have occurred in order to negate their effects has not yet been considered. This is in stark contrast with quantum computation proposals for Abelian anyons, for which decoding algorithms have been tailor-made for many topological error-correcting codes and error models. Here, we address this issue by considering the properties of non-Abelian error correction, in general. We also choose a specific anyon model and error model to probe the problem in more detail. The anyon model is the charge submodel of D(S_{3}. This shares many properties with important models such as the Fibonacci anyons, making our method more generally applicable. The error model is a straightforward generalization of those used in the case of Abelian anyons for initial benchmarking of error correction methods. It is found that error correction is possible under a threshold value of 7% for the total probability of an error on each physical spin. This is remarkably comparable with the thresholds for Abelian models.
Topics in Two-Dimensional Quantum Gravity and Chern-Simons Gauge Theories
Zemba, Guillermo Raul
A series of studies in two and three dimensional theories is presented. The two dimensional problems are considered in the framework of String Theory. The first one determines the region of integration in the space of inequivalent tori of a tadpole diagram in Closed String Field Theory, using the naive Witten three-string vertex. It is shown that every surface is counted an infinite number of times and the source of this behavior is identified. The second study analyzes the behavior of the discrete matrix model of two dimensional gravity without matter using a mathematically well-defined construction, confirming several conjectures and partial results from the literature. The studies in three dimensions are based on Chern Simons pure gauge theory. The first one deals with the projection of the theory onto a two-dimensional surface of constant time, whereas the second analyzes the large N behavior of the SU(N) theory and makes evident a duality symmetry between the only two parameters of the theory. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).
Energy Technology Data Exchange (ETDEWEB)
Ito, K R [Kyoto Univ. (Japan). Research Inst. for Mathematical Sciences
1975-03-01
The Schwinger model is considered in the Landau-gauge formalism of quantum electrodynamics. This model can be solved exactly on the assumption of no radiative corrections to the anomaly. It is found that the photon obtains a non-zero mass through the Higgs mechanism. In this case, the would-be Nambu-Goldstone boson is an associated boson which is constructed from a pair of two-component massless fermions. This would-be Nambu-Goldstone boson appears as a result of the spontaneous breaking of the gauge invariance of the first kind, and it becomes unphysical through the Higgs mechanism. However, as all the fermions themselves decouple from photons, they cannot appear as real particles in our world.
International Nuclear Information System (INIS)
Tamura, K.; Jansen, R. A.; Windhorst, R. A.; Eskridge, P. B.; Cohen, S. H.
2010-01-01
We present the results of a study of the late-type spiral galaxy NGC 0959, before and after application of the pixel-based dust extinction correction described in Tamura et al. (Paper I). Galaxy Evolution Explorer far-UV, and near-UV, ground-based Vatican Advanced Technology Telescope, UBVR, and Spitzer/Infrared Array Camera 3.6, 4.5, 5.8, and 8.0 μm images are studied through pixel color-magnitude diagrams and pixel color-color diagrams (pCCDs). We define groups of pixels based on their distribution in a pCCD of (B - 3.6 μm) versus (FUV - U) colors after extinction correction. In the same pCCD, we trace their locations before the extinction correction was applied. This shows that selecting pixel groups is not meaningful when using colors uncorrected for dust. We also trace the distribution of the pixel groups on a pixel coordinate map of the galaxy. We find that the pixel-based (two-dimensional) extinction correction is crucial for revealing the spatial variations in the dominant stellar population, averaged over each resolution element. Different types and mixtures of stellar populations, and galaxy structures such as a previously unrecognized bar, become readily discernible in the extinction-corrected pCCD and as coherent spatial structures in the pixel coordinate map.
Causal approach to (2+1)-dimensional Quantum Electrodynamics
International Nuclear Information System (INIS)
Scharf, G.; Wreszinski, W.F.; Pimentel, B.M.; Tomazelli, J.L.
1993-05-01
It is shown that the causal approach to (2+1)-dimensional quantum electrodynamics yields a well-defined perturbative theory. In particular, and in contrast to renormalized perturbative quantum field theory, it is free of any ambiguities and ascribes a nonzero value to the dynamically generated, nonperturbative photon mass. (author). 12 refs
Quantum hall fluid on fuzzy two dimensional sphere
International Nuclear Information System (INIS)
Luo Xudong; Peng Dantao
2004-01-01
After reviewing the Haldane's description about the quantum Hall effect on the fuzzy two-sphere S 2 , authors construct the noncommutative algebra on the fuzzy sphere S 2 and the Moyal structure of the Hilbert space. By constructing noncommutative Chern-Simons theory of the incompressible Hall fluid on the fuzzy sphere and solving the Gaussian constraint with quasiparticle source, authors find the Calogero matrix on S 2 and the complete set of the Laughlin wave function for the lowest Landau level, and this wave function is expressed by the generalized Jack polynomials in terms of spinor coordinates. (author)
The effect of quantum correction on plasma electron heating in ultraviolet laser interaction
Energy Technology Data Exchange (ETDEWEB)
Zare, S.; Sadighi-Bonabi, R., E-mail: Sadighi@sharif.ir; Anvari, A. [Department of Physics, Sharif University of Technology, P.O. Box 11365-9567, Tehran (Iran, Islamic Republic of); Yazdani, E. [Department of Energy Engineering and Physics, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran (Iran, Islamic Republic of); Hora, H. [Department of Theoretical Physics, University of New South Wales, Sydney 2052 (Australia)
2015-04-14
The interaction of the sub-picosecond UV laser in sub-relativistic intensities with deuterium is investigated. At high plasma temperatures, based on the quantum correction in the collision frequency, the electron heating and the ion block generation in plasma are studied. It is found that due to the quantum correction, the electron heating increases considerably and the electron temperature uniformly reaches up to the maximum value of 4.91 × 10{sup 7 }K. Considering the quantum correction, the electron temperature at the laser initial coupling stage is improved more than 66.55% of the amount achieved in the classical model. As a consequence, by the modified collision frequency, the ion block is accelerated quicker with higher maximum velocity in comparison with the one by the classical collision frequency. This study proves the necessity of considering a quantum mechanical correction in the collision frequency at high plasma temperatures.
Energy Technology Data Exchange (ETDEWEB)
Sukhanov, Aleksei A.
2017-05-15
We study the energy spectra of bound states in quantum dots (QDs) formed by an electrostatic potential in two-dimensional topological insulator (TI) and their transformation with changes in QD depth and radius. It is found that, unlike a trivial insulator, the energy difference between the levels of the ground state and first excited state can decrease with decreasing the radius and increasing the depth of the QD so that these levels intersect under some critical condition. The crossing of the levels results in unusual features of optical properties caused by intraceneter electron transitions. In particular, it leads to significant changes of light absorption due to electron transitions between such levels and to the transient electroluminescence induced by electrical tuning of QD and TI parameters. In the case of magnetic TIs, the polarization direction of the absorbed or emitted circularly polarized light is changed due to the level crossing.
Sukhanov, Aleksei A.
2017-05-01
We study the energy spectra of bound states in quantum dots (QDs) formed by an electrostatic potential in two-dimensional topological insulator (TI) and their transformation with changes in QD depth and radius. It is found that, unlike a trivial insulator, the energy difference between the levels of the ground state and first excited state can decrease with decreasing the radius and increasing the depth of the QD so that these levels intersect under some critical condition. The crossing of the levels results in unusual features of optical properties caused by intraceneter electron transitions. In particular, it leads to significant changes of light absorption due to electron transitions between such levels and to the transient electroluminescence induced by electrical tuning of QD and TI parameters. In the case of magnetic TIs, the polarization direction of the absorbed or emitted circularly polarized light is changed due to the level crossing.
Chakrabarti, S; Chatterjee, B; Debbarma, S; Ghatak, K P
2015-09-01
In this paper we study the influence of strong electric field on the two dimensional (2D)effective electron mass (EEM) at the Fermi level in quantum wells of III-V, ternary and quaternary semiconductors within the framework of k x p formalism by formulating a new 2D electron energy spectrum. It appears taking quantum wells of InSb, InAs, Hg(1-x)Cd(x)Te and In(1-x)Ga(x)As(1-y)P(y) lattice matched to InP as examples that the EEM increases with decreasing film thickness, increasing electric field and increases with increasing surface electron concentration exhibiting spikey oscillations because of the crossing over of the Fermi level by the quantized level in quantum wells and the quantized oscillation occurs when the Fermi energy touches the sub-band energy. The electric field makes the mass quantum number dependent and the oscillatory mass introduces quantum number dependent mass anisotropy in addition to energy. The EEM increases with decreasing alloy composition where the variations are totally band structure dependent. Under certain limiting conditions all the results for all the cases get simplified into the well-known parabolic energy bands and thus confirming the compatibility test. The content of this paper finds three applications in the fields of nano-science and technology.
Determination and Correction of Persistent Biases in Quantum Annealers
2016-08-25
for all of the qubits. Narrowing of the bias distribution. To show the correctability of the persistent biases , we ran the experiment described above...this is a promising application for bias correction . Importantly, while the J biases determined here are in general smaller than the h biases , numerical...1Scientific RepoRts | 6:18628 | DOI: 10.1038/srep18628 www.nature.com/scientificreports Determination and correction of persistent biases in quantum
Definition and evolution of quantum cellular automata with two qubits per cell
International Nuclear Information System (INIS)
Karafyllidis, Ioannis G.
2004-01-01
Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical systems and processes. It is however known that except for the trivial case, unitary evolution of one-dimensional homogeneous quantum cellular automata with one qubit per cell is not possible. Quantum cellular automata that comprise two qubits per cell are defined and their evolution is studied using a quantum computer simulator. The evolution is unitary and its linearity manifests itself as a periodic structure in the probability distribution patterns
Three-dimensional quantum key distribution in the presence of several eavesdroppers
International Nuclear Information System (INIS)
Daoud, M; Ez-zahraouy, H
2011-01-01
Quantum key distribution based on encoding in three-dimensional systems in the presence of several eavesdroppers is proposed. This extends the BB84 protocol in the presence of many eavesdroppers where two-level quantum systems (qubits) are replaced by three-level systems (qutrits). We discuss the scenarios involving two, three and four complementary bases. We derive the explicit form of Alice and Bob mutual information and the information gained by each eavesdropper. In particular, we show that, in the presence of only one eavesdropper, the protocol involving four bases is safer than the other ones. However, for two eavesdroppers, the security is strongly dependent on the attack probabilities. The effect of a large number of eavesdroppers is also investigated.
Three-dimensional quantum key distribution in the presence of several eavesdroppers
Energy Technology Data Exchange (ETDEWEB)
Daoud, M [Max Planck Institute for the Physics of Complex Systems, Dresden (Germany); Ez-zahraouy, H, E-mail: daoud@pks.mpg.de, E-mail: ezahamid@fsr.ac.m [LMPHE (URAC), Faculty of Sciences, University Mohammed V-Agdal, Rabat (Morocco)
2011-10-15
Quantum key distribution based on encoding in three-dimensional systems in the presence of several eavesdroppers is proposed. This extends the BB84 protocol in the presence of many eavesdroppers where two-level quantum systems (qubits) are replaced by three-level systems (qutrits). We discuss the scenarios involving two, three and four complementary bases. We derive the explicit form of Alice and Bob mutual information and the information gained by each eavesdropper. In particular, we show that, in the presence of only one eavesdropper, the protocol involving four bases is safer than the other ones. However, for two eavesdroppers, the security is strongly dependent on the attack probabilities. The effect of a large number of eavesdroppers is also investigated.
Synthetic electromagnetic knot in a three-dimensional skyrmion
Lee, Wonjae; Gheorghe, Andrei H.; Tiurev, Konstantin; Ollikainen, Tuomas; Möttönen, Mikko; Hall, David S.
2018-01-01
Classical electromagnetism and quantum mechanics are both central to the modern understanding of the physical world and its ongoing technological development. Quantum simulations of electromagnetic forces have the potential to provide information about materials and systems that do not have conveniently solvable theoretical descriptions, such as those related to quantum Hall physics, or that have not been physically observed, such as magnetic monopoles. However, quantum simulations that simul...
Quantum statistical entropy corresponding to cosmic horizon in five-dimensional spacetime
Institute of Scientific and Technical Information of China (English)
2008-01-01
The generalized uncertainty relation is introduced to calculate the quantum statis-tical entropy corresponding to cosmic horizon. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is no divergent logarithmic term in the original brick-wall method. And it is obtained that the quantum statistical en-tropy corresponding to cosmic horizon is proportional to the area of the horizon. Further it is shown that the entropy corresponding to cosmic horizon is the entropy of quantum state on the surface of horizon. The black hole’s entropy is the intrinsic property of the black hole. The entropy is a quantum effect. In our calculation, by using the quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of five-dimensional spacetime. We provide a way to study the quantum statistical entropy corresponding to cosmic horizon in the higher-dimensional spacetime.
Time-dependent behavior of D-dimensional ideal quantum gases
International Nuclear Information System (INIS)
Oh, Suhk Kun
1985-01-01
The time-dependent behavior of D-dimensional ideal quantum gases is studied within the Mori formalism and its extension by Lee. In the classical limit, the time-dependent behavior is found to be independent of the dimensionality D of the system and is characterized by an extremely damped Gaussian relaxation function. However, at T=0K, it depends on the particular statistics adopted for the system and also on the dimensionality of the system. For the ideal Bose gas at T=0 K, complete Bose condensation is manifested by collapse of the dimensionality of a Hilbert space, spanned by basis vectors fsub(ν), from infinity to two. On the other hand, the dimensional effect for the ideal Fermi gas is exhibited by a change in Hilbert space structure, which is determined by the recurrants Δsub(ν) and the basis vectors fsub(ν) More specifically, the structural form of the recurrants is modified such that the relaxation function becomes more damped as D is increased. (Author)
Error Correction using Quantum Quasi-Cyclic Low-Density Parity-Check(LDPC) Codes
Jing, Lin; Brun, Todd; Quantum Research Team
Quasi-cyclic LDPC codes can approach the Shannon capacity and have efficient decoders. Manabu Hagiwara et al., 2007 presented a method to calculate parity check matrices with high girth. Two distinct, orthogonal matrices Hc and Hd are used. Using submatrices obtained from Hc and Hd by deleting rows, we can alter the code rate. The submatrix of Hc is used to correct Pauli X errors, and the submatrix of Hd to correct Pauli Z errors. We simulated this system for depolarizing noise on USC's High Performance Computing Cluster, and obtained the block error rate (BER) as a function of the error weight and code rate. From the rates of uncorrectable errors under different error weights we can extrapolate the BER to any small error probability. Our results show that this code family can perform reasonably well even at high code rates, thus considerably reducing the overhead compared to concatenated and surface codes. This makes these codes promising as storage blocks in fault-tolerant quantum computation. Error Correction using Quantum Quasi-Cyclic Low-Density Parity-Check(LDPC) Codes.
Three dimensional topography correction applied to magnetotelluric data from Sikkim Himalayas
Kumar, Sushil; Patro, Prasanta K.; Chaudhary, B. S.
2018-06-01
Magnetotelluric (MT) method is one of the powerful tools to investigate the deep crustal image of mountainous regions such as Himalayas. Topographic variations due to irregular surface terrain distort the resistivity curves and hence may not give accurate interpretation of magnetotelluric data. The two-dimensional (2-D) topographic effects in Transverse Magnetic (TM) mode is only galvanic whereas inductive in Transverse Electric (TE) mode, thus TM mode responses is much more important than TE mode responses in 2-D. In three-dimensional (3-D), the topography effect is both galvanic and inductive in each element of impedance tensor and hence the interpretation is complicated. In the present work, we investigate the effects of three-dimensional (3-D) topography for a hill model. This paper presents the impedance tensor correction algorithm to reduce the topographic effects in MT data. The distortion caused by surface topography effectively decreases by using homogeneous background resistivity in impedance correction method. In this study, we analyze the response of ramp, distance from topographic edges, conductive and resistive dykes. The new correction method is applied to the real data from Sikkim Himalayas, which brought out the true nature of the basement in this region.
The two-loop renormalization of general quantum field theories
International Nuclear Information System (INIS)
Damme, R.M.J. van.
1984-01-01
This thesis provides a general method to compute all first order corrections to the renormalization group equations. This requires the computation of the first perturbative corrections to the renormalization group β-functions. These corrections are described by Feynman diagrams with two loops. The two-loop renormalization is treated for an arbitrary renormalization field theory. Two cases are considered: 1. the Yukawa sector; 2. the gauge coupling and the scalar potential. In a final section, the breakdown of unitarity in the dimensional reduction scheme is discussed. (Auth.)
Two-dimensional topological photonic systems
Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng
2017-09-01
The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.
We live in the quantum 4-dimensional Minkowski space-time
Hwang, W-Y. Pauchy
2015-01-01
We try to define "our world" by stating that "we live in the quantum 4-dimensional Minkowski space-time with the force-fields gauge group $SU_c(3) \\times SU_L(2) \\times U(1) \\times SU_f(3)$ built-in from the outset". We begin by explaining what "space" and "time" are meaning for us - the 4-dimensional Minkowski space-time, then proceeding to the quantum 4-dimensional Minkowski space-time. In our world, there are fields, or, point-like particles. Particle physics is described by the so-called ...
Quantum gravitational corrections for spinning particles
International Nuclear Information System (INIS)
Fröb, Markus B.
2016-01-01
We calculate the quantum corrections to the gauge-invariant gravitational potentials of spinning particles in flat space, induced by loops of both massive and massless matter fields of various types. While the corrections to the Newtonian potential induced by massless conformal matter for spinless particles are well known, and the same corrections due to massless minimally coupled scalars http://dx.doi.org/10.1088/0264-9381/27/24/245008, massless non-conformal scalars http://dx.doi.org/10.1103/PhysRevD.87.104027 and massive scalars, fermions and vector bosons http://dx.doi.org/10.1103/PhysRevD.91.064047 have been recently derived, spinning particles receive additional corrections which are the subject of the present work. We give both fully analytic results valid for all distances from the particle, and present numerical results as well as asymptotic expansions. At large distances from the particle, the corrections due to massive fields are exponentially suppressed in comparison to the corrections from massless fields, as one would expect. However, a surprising result of our analysis is that close to the particle itself, on distances comparable to the Compton wavelength of the massive fields running in the loops, these corrections can be enhanced with respect to the massless case.
Vector current scattering in two dimensional quantum chromodynamics
International Nuclear Information System (INIS)
Fleishon, N.L.
1979-04-01
The interaction of vector currents with hadrons is considered in a two dimensional SU(N) color gauge theory coupled to fermions in leading order in an N -1 expansion. After giving a detailed review of the model, various transition matrix elements of one and two vector currents between hadronic states were considered. A pattern is established whereby the low mass currents interact via meson dominance and the highly virtual currents interact via bare quark-current couplings. This pattern is especially evident in the hadronic contribution to inelastic Compton scattering, M/sub μν/ = ∫ dx e/sup iq.x/ , which is investigated in various kinematic limits. It is shown that in the dual Regge region of soft processes the currents interact as purely hadronic systems. Modification of dimensional counting rules is indicated by a study of a large angle scattering analog. In several hard inclusive nonlight cone processes, parton model ideas are confirmed. The impulse approximation is valid in a Bjorken--Paschos-like limit with very virtual currents. A Drell--Yan type annihilation mechanism is found in photoproduction of massive lepton pairs, leading to identification of a parton wave function for the current. 56 references
Experiments on two-resonator circuit quantum electrodynamics. A superconducting quantum switch
Energy Technology Data Exchange (ETDEWEB)
Hoffmann, Elisabeth Christiane Maria
2013-05-29
The field of cavity quantum electrodynamics (QED) studies the interaction between light and matter on a fundamental level. In typical experiments individual natural atoms are interacting with individual photons trapped in three-dimensional cavities. Within the last decade the prospering new field of circuit QED has been developed. Here, the natural atoms are replaced by artificial solid state quantum circuits offering large dipole moments which are coupled to quasi-onedimensional cavities providing a small mode volume and hence a large vacuum field strength. In our experiments Josephson junction based superconducting quantum bits are coupled to superconducting microwave resonators. In circuit QED the number of parameters that can be varied is increased and regimes that are not accessible using natural atoms can be entered and investigated. Apart from design flexibility and tunability of system parameters a particular advantage of circuit QED is the scalability to larger system size enabled by well developed micro- and nanofabrication tools. When scaling up the resonator-qubit systems beyond a few coupled circuits, the rapidly increasing number of interacting subsystems requires an active control and directed transmission of quantum signals. This can, for example, be achieved by implementing switchable coupling between two microwave resonators. To this end, a superconducting flux qubit is used to realize a suitable coupling between two microwave resonators, all working in the Gigahertz regime. The resulting device is called quantum switch. The flux qubit mediates a second order tunable and switchable coupling between the resonators. Depending on the qubit state, this coupling can compensate for the direct geometric coupling of the two resonators. As the qubit may also be in a quantum superposition state, the switch itself can be ''quantum'': it can be a superposition of ''on'' and ''off''. This work
Dolan Grady relations and noncommutative quasi-exactly solvable systems
Klishevich, Sergey M.; Plyushchay, Mikhail S.
2003-11-01
We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the {\\mathfrak{su}}(2) and {\\mathfrak{sl}}(2,{\\bb {R}}) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.
Three-dimensionality of space and the quantum bit: an information-theoretic approach
International Nuclear Information System (INIS)
Müller, Markus P; Masanes, Lluís
2013-01-01
It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry ‘minimal amounts of direction information’, interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d = 3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements. (paper)
Aspects of quantum corrections in a Lorentz-violating extension of the abelian Higgs Model
Energy Technology Data Exchange (ETDEWEB)
Brito, L.C.T.; Fargnoli, H.G. [Universidade Federal de Lavras, MG (Brazil); Scarpelli, A.P. Baeta [Departamento de Policia Federal, Rio de Janeiro, RJ (Brazil)
2013-07-01
Full text: We have investigated new aspects related to the four-dimensional abelian gauge-Higgs model with the addition of the Carroll-Field-Jackiw term (CFJ). We have focused on one-loop quantum corrections to the photon and Higgs sectors and we have analyzed what kind of effects are induced at the quantum level by spontaneous gauge symmetry breaking due the presence of the CFJ term. We have shown that new finite and non-ambiguous Lorentz-breaking terms are induced in both sectors at second order in the background vector. Specifically in the pure gauge sector, a CPT-even aether term (free from ambiguities) is induced. A CPT-even term is also induced in the pure Higgs sector. Both terms have been mapped in the Standard Model Extension. Besides, aspects of the one-loop renormalization of the background vector dependent terms have been studied. The new divergences due the presence of the CFJ term were shown to be worked out by the renormalization condition which requires the vanishing of the vacuum expectation value of the Higgs field. So at one loop the CFJ term does not spoil the well known renormalizability of the model without Lorentz symmetry breaking terms. The calculations have been done within dimensional methods and in an arbitrary gauge choice. (author)
Skyrmion burst and multiple quantum walk in thin ferromagnetic films
International Nuclear Information System (INIS)
Ezawa, Motohiko
2011-01-01
We propose a new type of quantum walk in thin ferromagnetic films. A giant Skyrmion collapses to a singular point in a thin ferromagnetic film, emitting spin waves, when external magnetic field is increased beyond the critical one. After the collapse the remnant is a quantum walker carrying spin S. We determine its time evolution and show the diffusion process is a continuous-time quantum walk. We also analyze an interference of two quantum walkers after two Skyrmion bursts. The system presents a new type of quantum walk for S>1/2, where a quantum walker breaks into 2S quantum walkers. -- Highlights: → A giant Skyrmion collapses to a singular point by applying strong magnetic field. → Quantum walk is realized in thin ferromagnetic films by Skyrmion collapsing. → Quantum walks for S=1/2 and 1 are exact solvable, where S represents the spin. → Quantum walks for >1/2 presents a new type of quantum walks, i.e., 'multiple quantum walks'. → Skyrmion bursts which occur simultaneously exhibit an interference as a manifestation of quantum walk.
International Nuclear Information System (INIS)
Sparenberg, Jean-Marc; Samsonov, Boris F; Foucart, Francois; Baye, Daniel
2006-01-01
A new type of supersymmetric transformations of the coupled-channel radial Schroedinger equation is introduced, which do not conserve the vanishing behaviour of solutions at the origin. Contrary to the usual transformations, these 'non-conservative' transformations allow, in the presence of thresholds, the construction of well-behaved potentials with coupled scattering matrices from uncoupled potentials. As an example, an exactly-solvable potential matrix is obtained which provides a very simple model of the Feshbach-resonance phenomenon. (letter to the editor)
Terahertz magneto-optical spectroscopy of a two-dimensional hole gas
Energy Technology Data Exchange (ETDEWEB)
Kamaraju, N., E-mail: nkamaraju@lanl.gov; Taylor, A. J.; Prasankumar, R. P., E-mail: rpprasan@lanl.gov [Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Pan, W.; Reno, J. [Sandia National Laboratories, Albuquerque, New Mexico 87123 (United States); Ekenberg, U. [Semiconsultants, Brunnsgrnd 12, SE-18773 Täby (Sweden); Gvozdić, D. M. [School of Electrical Engineering, University of Belgrade, Belgrade 11120 (Serbia); Boubanga-Tombet, S. [Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-Ku, Sendai (Japan); Upadhya, P. C. [Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Laboratory for Electro-Optics Systems, Indian Space Research Organization, Bangalore 560058 (India)
2015-01-19
Two-dimensional hole gases (2DHGs) have attracted recent attention for their unique quantum physics and potential applications in areas including spintronics and quantum computing. However, their properties remain relatively unexplored, motivating the use of different techniques to study them. We used terahertz magneto-optical spectroscopy to investigate the cyclotron resonance frequency in a high mobility 2DHG, revealing a nonlinear dependence on the applied magnetic field. This is shown to be due to the complex non-parabolic valence band structure of the 2DHG, as verified by multiband Landau level calculations. We also find that impurity scattering dominates cyclotron resonance decay in the 2DHG, in contrast with the dominance of superradiant damping in two-dimensional electron gases. Our results shed light on the properties of 2DHGs, motivating further studies of these unique 2D nanosystems.
Energy Technology Data Exchange (ETDEWEB)
Hyakutake, Yoshifumi [Faculty of Science, Ibaraki University,Bunkyo 2-1-1, Mito, Ibaraki, 310-8512 (Japan)
2015-09-11
We take into account higher derivative R{sup 4} corrections in M-theory and construct quantum black hole and black string solutions in 11 dimensions up to the next leading order. The quantum black string is stretching along the 11th direction and the Gregory-Laflamme instability is examined at the quantum level. Thermodynamics of the boosted quantum black hole and black string are also discussed. Especially we take the near horizon limit of the quantum black string and investigate its instability quantitatively.
A protocol for the secure two-party quantum scalar product
Energy Technology Data Exchange (ETDEWEB)
He, Li-Bao, E-mail: helibao@mail.ustc.edu.cn [National High Performance Computing Center, Department of Computer Science and Technology, USTC, Hefei 230027 (China); Suzhou Institute for Advanced Study, USTC, Suzhou 215123 (China); Huang, Liu-Sheng; Yang, Wei; Xu, Rui [National High Performance Computing Center, Department of Computer Science and Technology, USTC, Hefei 230027 (China); Suzhou Institute for Advanced Study, USTC, Suzhou 215123 (China)
2012-03-19
Secure scalar product serves as an important primitive for secure multi-party computation and has a wide application in different areas, such as statistical analysis, data mining, computational geometry, etc. How to collaboratively compute the correct scalar product result without leaking any participants' private information becomes the primary principle of designing secure scalar product schemes. In this Letter, we present a secure two-party quantum scalar product scheme via quantum entanglement and quantum measurement with the help of a non-colluding third party (TP). Furthermore, the scheme is proven to be secure under various kinds of outside attacks and participant attacks. -- Highlights: ► We extend the secure two-party scalar product to the quantum field. ► Our protocol is built upon quantum entanglement and quantum measurement. ► Communication cost is acceptable if the elements of participants' private vectors are not too sparse. ► Participants will leak no private information under the no-collusion model.
A protocol for the secure two-party quantum scalar product
International Nuclear Information System (INIS)
He, Li-Bao; Huang, Liu-Sheng; Yang, Wei; Xu, Rui
2012-01-01
Secure scalar product serves as an important primitive for secure multi-party computation and has a wide application in different areas, such as statistical analysis, data mining, computational geometry, etc. How to collaboratively compute the correct scalar product result without leaking any participants' private information becomes the primary principle of designing secure scalar product schemes. In this Letter, we present a secure two-party quantum scalar product scheme via quantum entanglement and quantum measurement with the help of a non-colluding third party (TP). Furthermore, the scheme is proven to be secure under various kinds of outside attacks and participant attacks. -- Highlights: ► We extend the secure two-party scalar product to the quantum field. ► Our protocol is built upon quantum entanglement and quantum measurement. ► Communication cost is acceptable if the elements of participants' private vectors are not too sparse. ► Participants will leak no private information under the no-collusion model.
International Nuclear Information System (INIS)
Gong, Longyan; Zhu, Hao; Zhao, Shengmei; Cheng, Weiwen; Sheng, Yubo
2012-01-01
We investigate numerically the quantum discord and the classical correlation in a one-dimensional slowly varying potential model and a one-dimensional Soukoulis–Economou ones, respectively. There are well-defined mobility edges in the slowly varying potential model, while there are discrepancies on mobility edges in the Soukoulis–Economou ones. In the slowly varying potential model, we find that extended and localized states can be distinguished by both the quantum discord and the classical correlation. There are sharp transitions in the quantum discord and the classical correlation at mobility edges. Based on these, we study “mobility edges” in the Soukoulis–Economou model using the quantum discord and the classical correlation, which gives another perspectives for these “mobility edges”. All these provide us good quantities, i.e., the quantum discord and the classical correlation, to reflect mobility edges in these one-dimensional aperiodic single-electron systems. Moreover, our studies propose a consistent interpretation of the discrepancies between previous numerical results about the Soukoulis–Economou model. -- Highlights: ► Quantum discord and classical correlation can signal mobility edges in two models. ► An interpretation for mobility edges in the Soukoulis–Economou model is proposed. ► Quantum discord and classical correlation can reflect well localization properties.
Renner, R; Cirac, J I
2009-03-20
We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks.
Quantum pump effect induced by a linearly polarized microwave in a two-dimensional electron gas.
Song, Juntao; Liu, Haiwen; Jiang, Hua
2012-05-30
A quantum pump effect is predicted in an ideal homogeneous two-dimensional electron gas (2DEG) that is normally irradiated by linearly polarized microwaves (MW). Without considering effects from spin-orbital coupling or the magnetic field, it is found that a polarized MW can continuously pump electrons from the longitudinal to the transverse direction, or from the transverse to the longitudinal direction, in the central irradiated region. The large pump current is obtained for both the low frequency limit and the high frequency case. Its magnitude depends on sample properties such as the size of the radiated region, the power and frequency of the MW, etc. Through the calculated results, the pump current should be attributed to the dominant photon-assisted tunneling processes as well as the asymmetry of the electron density of states with respect to the Fermi energy.
Families of superintegrable Hamiltonians constructed from exceptional polynomials
International Nuclear Information System (INIS)
Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc
2012-01-01
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable. (paper)
Stopping time of a one-dimensional bounded quantum walk
International Nuclear Information System (INIS)
Luo Hao; Zhang Peng; Zhan Xiang; Xue Peng
2016-01-01
The stopping time of a one-dimensional bounded classical random walk (RW) is defined as the number of steps taken by a random walker to arrive at a fixed boundary for the first time. A quantum walk (QW) is a non-trivial generalization of RW, and has attracted a great deal of interest from researchers working in quantum physics and quantum information. In this paper, we develop a method to calculate the stopping time for a one-dimensional QW. Using our method, we further compare the properties of stopping time for QW and RW. We find that the mean value of the stopping time is the same for both of these problems. However, for short times, the probability for a walker performing a QW to arrive at the boundary is larger than that for a RW. This means that, although the mean stopping time of a quantum and classical walker are the same, the quantum walker has a greater probability of arriving at the boundary earlier than the classical walker. (paper)
Quantum localization in the three-dimensional kicked Rydberg atom
International Nuclear Information System (INIS)
Persson, Emil; Yoshida, Shuhei; Burgdoerfer, Joachim; Tong, X.-M.; Reinhold, Carlos O.
2003-01-01
We study the three-dimensional (3D) unidirectionally kicked Rydberg atom. For parabolic initial states elongated in the direction of the kicks we show that the ionization of the quantum system is suppressed as compared to the classical counterpart and that the quantum wave function is localized along all degrees of freedom, whereas the classical system is globally diffusive. We discuss the connection to the previously studied one-dimensional (1D) model of the kicked Rydberg atom and verify that the 1D model is a good approximation to the 3D quantum case in the limiting case of the most elongated initial states. We further study the quantum phase-space distribution (Husimi distribution) of the eigenstates of the period-one time-evolution (Floquet) operator and show that the eigenstates are localized in phase space. For the most elongated parabolic initial state, we are able to identify the unstable periodic orbits around which Floquet states localize. We discuss the possibility of observing quantum localization in high Rydberg states in n>100
Jaschke, Daniel; Wall, Michael L.; Carr, Lincoln D.
2018-04-01
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States (MPSs), have attracted interest from different fields of quantum physics ranging from solid state systems to quantum simulators and quantum computing. Our open source MPS code provides the community with a toolset to analyze the statics and dynamics of one-dimensional quantum systems. Here, we present our open source library, Open Source Matrix Product States (OSMPS), of MPS methods implemented in Python and Fortran2003. The library includes tools for ground state calculation and excited states via the variational ansatz. We also support ground states for infinite systems with translational invariance. Dynamics are simulated with different algorithms, including three algorithms with support for long-range interactions. Convenient features include built-in support for fermionic systems and number conservation with rotational U(1) and discrete Z2 symmetries for finite systems, as well as data parallelism with MPI. We explain the principles and techniques used in this library along with examples of how to efficiently use the general interfaces to analyze the Ising and Bose-Hubbard models. This description includes the preparation of simulations as well as dispatching and post-processing of them.
Flatland Position-Dependent-Mass: Polar Coordinates, Separability and Exact Solvability
Directory of Open Access Journals (Sweden)
Omar Mustafa
2010-10-01
Full Text Available The kinetic energy operator with position-dependent-mass in plane polar coordinates is obtained. The separability of the corresponding Schrödinger equation is discussed. A hypothetical toy model is reported and two exactly solvable examples are studied.
Quantum cryptography: individual eavesdropping with the knowledge of the error-correcting protocol
International Nuclear Information System (INIS)
Horoshko, D B
2007-01-01
The quantum key distribution protocol BB84 combined with the repetition protocol for error correction is analysed from the point of view of its security against individual eavesdropping relying on quantum memory. It is shown that the mere knowledge of the error-correcting protocol changes the optimal attack and provides the eavesdropper with additional information on the distributed key. (fifth seminar in memory of d.n. klyshko)
Quantum Fluctuations of Low Dimensional Bose-Einstein ...
African Journals Online (AJOL)
Tadesse
that low dimensional quantum gases exhibit not only highly fascinating .... 2009; Marquardt and Girvin, 2009; Law, 1995; Vitali et al., 2007). ... ideal playground to test correlations between light and mesoscopic objects, to understand the.
Model of tunnelling through periodic array of quantum dots
Directory of Open Access Journals (Sweden)
Meynster Dmitry
2017-01-01
Full Text Available Several explicitly solvable models of electron tunnelling in a system of single and double two-dimensional periodic arrays of quantum dots with two laterally coupled leads in a homogeneous magnetic field are constructed. First, a model of single layer formed by periodic array of zero-range potentials is described. The Landau operator (the Schrodinger operator with a magnetic field with point-like interactions is the system Hamiltonian. We deal with two types of the layer lattices: square and honeycomb. The periodicity condition gives one an invariance property for the Hamiltonian in respect to magnetic translations group. The consideration of double quantum layer reduces to the replacement of the basic cell for the single layer by a cell including centers of different layers. Two variants of themodel for the double layer are suggested: with direct tunneling between the layers and with the connecting channels (segments in the model between the layers. The theory of self-adjoint extensions of symmetric operators is a mathematical background of the model. The third stage of the construction is the description of leads connection. It is made by the operator extensions theory method too. Electron tunneling from input lead to the output lead through the double quantum layer is described. Energy ranges with extremely small (practically, zero transmission were found. Dependencies of the transmission coefficient (particularly, “zero transmission bands” positions on the magnetic field, the energy of electron and the distance between layers are investigated. The results are compared with the corresponding single-layer transmission.
Quantum Corrected Non-Thermal Radiation Spectrum from the Tunnelling Mechanism
Directory of Open Access Journals (Sweden)
Subenoy Chakraborty
2015-06-01
Full Text Available The tunnelling mechanism is today considered a popular and widely used method in describing Hawking radiation. However, in relation to black hole (BH emission, this mechanism is mostly used to obtain the Hawking temperature by comparing the probability of emission of an outgoing particle with the Boltzmann factor. On the other hand, Banerjee and Majhi reformulated the tunnelling framework deriving a black body spectrum through the density matrix for the outgoing modes for both the Bose-Einstein distribution and the Fermi-Dirac distribution. In contrast, Parikh and Wilczek introduced a correction term performing an exact calculation of the action for a tunnelling spherically symmetric particle and, as a result, the probability of emission of an outgoing particle corresponds to a non-strictly thermal radiation spectrum. Recently, one of us (C. Corda introduced a BH effective state and was able to obtain a non-strictly black body spectrum from the tunnelling mechanism corresponding to the probability of emission of an outgoing particle found by Parikh and Wilczek. The present work introduces the quantum corrected effective temperature and the corresponding quantum corrected effective metric is written using Hawking’s periodicity arguments. Thus, we obtain further corrections to the non-strictly thermal BH radiation spectrum as the final distributions take into account both the BH dynamical geometry during the emission of the particle and the quantum corrections to the semiclassical Hawking temperature.
DEFF Research Database (Denmark)
da Lio, Beatrice; Bacco, Davide; Ding, Yunhong
2017-01-01
We experimentally prove a novel two-dimensional QKD scheme, relying on differential phasetime shifting (DPTS) of strongly attenuated weak coherent pulses. We demonstrate QKD transmission up to 170 km standard fiber, and even include a classical channel up to 90 km.......We experimentally prove a novel two-dimensional QKD scheme, relying on differential phasetime shifting (DPTS) of strongly attenuated weak coherent pulses. We demonstrate QKD transmission up to 170 km standard fiber, and even include a classical channel up to 90 km....
Two-dimensionally confined topological edge states in photonic crystals
International Nuclear Information System (INIS)
Barik, Sabyasachi; Miyake, Hirokazu; DeGottardi, Wade; Waks, Edo; Hafezi, Mohammad
2016-01-01
We present an all-dielectric photonic crystal structure that supports two-dimensionally confined helical topological edge states. The topological properties of the system are controlled by the crystal parameters. An interface between two regions of differing band topologies gives rise to topological edge states confined in a dielectric slab that propagate around sharp corners without backscattering. Three-dimensional finite-difference time-domain calculations show these edges to be confined in the out-of-plane direction by total internal reflection. Such nanoscale photonic crystal architectures could enable strong interactions between photonic edge states and quantum emitters. (paper)
On quantum corrected Kahler potentials in F-theory
García-Etxebarria, Iñaki; Savelli, Raffaele; Shiu, Gary
2013-01-01
We work out the exact in string coupling and perturbatively exact in \\alpha' result for the vector multiplet moduli K\\"ahler potential in a specific N=2 compactification of F-theory. The well-known correction cubic in {\\alpha}' is absent, but there is a rich structure of corrections at all even orders in \\alpha'. Moreover, each of these orders independently displays an SL(2,Z) invariant set of corrections in the string coupling. This generalizes earlier findings to the case of a non-trivial elliptic fibration. Our results pave the way for the analysis of quantum corrections in the more complicated N=1 context, and may have interesting implications for the study of moduli stabilization in string theory.
Mano, Tomohiro; Ohtsuki, Tomi
2017-11-01
The three-dimensional Anderson model is a well-studied model of disordered electron systems that shows the delocalization-localization transition. As in our previous papers on two- and three-dimensional (2D, 3D) quantum phase transitions [J. Phys. Soc. Jpn. 85, 123706 (2016), 86, 044708 (2017)], we used an image recognition algorithm based on a multilayered convolutional neural network. However, in contrast to previous papers in which 2D image recognition was used, we applied 3D image recognition to analyze entire 3D wave functions. We show that a full phase diagram of the disorder-energy plane is obtained once the 3D convolutional neural network has been trained at the band center. We further demonstrate that the full phase diagram for 3D quantum bond and site percolations can be drawn by training the 3D Anderson model at the band center.
Architectures for Quantum Simulation Showing a Quantum Speedup
Bermejo-Vega, Juan; Hangleiter, Dominik; Schwarz, Martin; Raussendorf, Robert; Eisert, Jens
2018-04-01
One of the main aims in the field of quantum simulation is to achieve a quantum speedup, often referred to as "quantum computational supremacy," referring to the experimental realization of a quantum device that computationally outperforms classical computers. In this work, we show that one can devise versatile and feasible schemes of two-dimensional, dynamical, quantum simulators showing such a quantum speedup, building on intermediate problems involving nonadaptive, measurement-based, quantum computation. In each of the schemes, an initial product state is prepared, potentially involving an element of randomness as in disordered models, followed by a short-time evolution under a basic translationally invariant Hamiltonian with simple nearest-neighbor interactions and a mere sampling measurement in a fixed basis. The correctness of the final-state preparation in each scheme is fully efficiently certifiable. We discuss experimental necessities and possible physical architectures, inspired by platforms of cold atoms in optical lattices and a number of others, as well as specific assumptions that enter the complexity-theoretic arguments. This work shows that benchmark settings exhibiting a quantum speedup may require little control, in contrast to universal quantum computing. Thus, our proposal puts a convincing experimental demonstration of a quantum speedup within reach in the near term.
Variational model for one-dimensional quantum magnets
Kudasov, Yu. B.; Kozabaranov, R. V.
2018-04-01
A new variational technique for investigation of the ground state and correlation functions in 1D quantum magnets is proposed. A spin Hamiltonian is reduced to a fermionic representation by the Jordan-Wigner transformation. The ground state is described by a new non-local trial wave function, and the total energy is calculated in an analytic form as a function of two variational parameters. This approach is demonstrated with an example of the XXZ-chain of spin-1/2 under a staggered magnetic field. Generalizations and applications of the variational technique for low-dimensional magnetic systems are discussed.
Solvable Family of Driven-Dissipative Many-Body Systems
Foss-Feig, Michael; Young, Jeremy T.; Albert, Victor V.; Gorshkov, Alexey V.; Maghrebi, Mohammad F.
2017-11-01
Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.
Elementary quantum field theory
International Nuclear Information System (INIS)
Thirring, W.; Henley, E.M.
1975-01-01
The first section of the book deals with the mathematical and physical description of a quantum field with the Bose-Einstein statistics and discusses observables, invariants of the field, and inner symmetries. The second section develops further methods for solvable interactions of a quantum field with static source. Section 3 explains with the aid of the Chew-Low model especially pion-nucleon scattering, static properties of nucleons, electromagnetic phenomena, and nuclear forces. (BJ/LN) [de
Multi-dimensional photonic states from a quantum dot
Lee, J. P.; Bennett, A. J.; Stevenson, R. M.; Ellis, D. J. P.; Farrer, I.; Ritchie, D. A.; Shields, A. J.
2018-04-01
Quantum states superposed across multiple particles or degrees of freedom offer an advantage in the development of quantum technologies. Creating these states deterministically and with high efficiency is an ongoing challenge. A promising approach is the repeated excitation of multi-level quantum emitters, which have been shown to naturally generate light with quantum statistics. Here we describe how to create one class of higher dimensional quantum state, a so called W-state, which is superposed across multiple time bins. We do this by repeated Raman scattering of photons from a charged quantum dot in a pillar microcavity. We show this method can be scaled to larger dimensions with no reduction in coherence or single-photon character. We explain how to extend this work to enable the deterministic creation of arbitrary time-bin encoded qudits.
International Nuclear Information System (INIS)
El-Hussein, K.
1991-08-01
Let V be a real finite dimensional vector space and let K be a connected compact Lie group, which acts on V by means of a continuous linear representation ρ. Let G=V x p K be the motion group which is the semi-direct product of V by K and let P be an invariant differential operator on G. In this paper we give a necessary and sufficient condition for the global solvability of P on G. Now let G be a connected semi-simple Lie group with finite centre and let P be an invariant differential operator on G. We give also a necessary and sufficient condition for the global solvability of P on G. (author). 8 refs
Dimensional regularization and infrared divergences in quantum electrodynamics
International Nuclear Information System (INIS)
Marculescu, S.
1979-01-01
Dimensional continuation was devised as a powerful regularization method for ultraviolet divergences in quantum field theories. Recently it was clear, at least for quantum electrodynamics, that such a method could be employed for factorizing out infrared divergences from the on-shell S-matrix elements. This provides a renormalization scheme on the electron mass-shell without using a gauge violating ''photon mass''. (author)
Quantum Corrections in Nanoplasmonics: Shape, Scale, and Material
DEFF Research Database (Denmark)
Christensen, Thomas; Yan, Wei; Jauho, Antti-Pekka
2017-01-01
The classical treatment of plasmonics is insufficient at the nanometer-scale due to quantum mechanical surface phenomena. Here, an extension of the classical paradigm is reported which rigorously remedies this deficiency through the incorporation of first-principles surface response functions......-the Feibelman d parameters-in general geometries. Several analytical results for the leading-order plasmonic quantum corrections are obtained in a first-principles setting; particularly, a clear separation of the roles of shape, scale, and material is established. The utility of the formalism is illustrated...
GEOMETRIZATION OF NONHOLONOMIC MECHANICAL SYSTEMS AND THEIR SOLVABILITY
Institute of Scientific and Technical Information of China (English)
慕小武; 郭仲衡
1990-01-01
A new geometrization approach to nonholonomic mechanical systems is proposed and a series of solvability conditions under the proposed geometric frame are given. The proposed frame differs essentially from Hermann’s. The limitations of Hermann’s frame are also discussed. It is shown that a system under Hermann’s frame is solvable only if its constraints are given by natural conservation laws of the corresponding constraint-free system.
Quantum fluctuations and spontaneous compactification of eleven-dimensional gravity
International Nuclear Information System (INIS)
Nguen Van Hieu.
1985-01-01
The reduction of the eleven-dimensional pure gravity to the field theory in the four-dimensional Minkowski space-time by means of the spontaneous compactification of the extra dimensions is investigated. The contribution of the quantum fluctuations of the eleven-dimen-- sonal second rank symmetric tensor field to the curvatures of the space-time and the compactified space of the extra dimensions are calculated in the one-loop approximation. It is shown that there exist the values of the cosmological constant for which tachions are absent. As a result, self-consistent quantum field theory is obtained in spontaneous compactified Minkowski space M 4 xS 7 ,is where M 4 is Minkowski space-time, and S 7 is seven-dimensional sphere
Metric dimensional reduction at singularities with implications to Quantum Gravity
International Nuclear Information System (INIS)
Stoica, Ovidiu Cristinel
2014-01-01
A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being just non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained
Quantum Effects in the Thermoelectric Power Factor of Low-Dimensional Semiconductors.
Hung, Nguyen T; Hasdeo, Eddwi H; Nugraha, Ahmad R T; Dresselhaus, Mildred S; Saito, Riichiro
2016-07-15
We theoretically investigate the interplay between the confinement length L and the thermal de Broglie wavelength Λ to optimize the thermoelectric power factor of semiconducting materials. An analytical formula for the power factor is derived based on the one-band model assuming nondegenerate semiconductors to describe quantum effects on the power factor of the low-dimensional semiconductors. The power factor is enhanced for one- and two-dimensional semiconductors when L is smaller than Λ of the semiconductors. In this case, the low-dimensional semiconductors having L smaller than their Λ will give a better thermoelectric performance compared to their bulk counterpart. On the other hand, when L is larger than Λ, bulk semiconductors may give a higher power factor compared to the lower dimensional ones.
Dirac Equation in (1 +1 )-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model
Pedernales, J. S.; Beau, M.; Pittman, S. M.; Egusquiza, I. L.; Lamata, L.; Solano, E.; del Campo, A.
2018-04-01
We introduce an exact mapping between the Dirac equation in (1 +1 )-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1 +1 )-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1 +1 )-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.
Topological quantum error correction in the Kitaev honeycomb model
Lee, Yi-Chan; Brell, Courtney G.; Flammia, Steven T.
2017-08-01
The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of topological quantum codes that are typically studied, but its exact solubility makes it more amenable to analysis of effects arising in this noncommutative setting than a generic topologically ordered Hamiltonian. Here we study quantum error correction in the honeycomb model using both analytic and numerical techniques. We first prove explicit exponential bounds on the approximate degeneracy, local indistinguishability, and correctability of the code space. These bounds are tighter than can be achieved using known general properties of topological phases. Our proofs are specialized to the honeycomb model, but some of the methods may nonetheless be of broader interest. Following this, we numerically study noise caused by thermalization processes in the perturbative regime close to the toric code renormalization group fixed point. The appearance of non-topological excitations in this setting has no significant effect on the error correction properties of the honeycomb model in the regimes we study. Although the behavior of this model is found to be qualitatively similar to that of the standard toric code in most regimes, we find numerical evidence of an interesting effect in the low-temperature, finite-size regime where a preferred lattice direction emerges and anyon diffusion is geometrically constrained. We expect this effect to yield an improvement in the scaling of the lifetime with system size as compared to the standard toric code.