Equivariant spectral triples on the quantum SU(2) group
Chakraborty, Partha Sarathi; Pal, Arupkumar
2002-01-01
We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L_2-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SU_q(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that...
Spectral triples and associated Connes-de Rham complex for the quantum SU(2) and the quantum sphere
Chakraborty, Partha Sarathi; Pal, Arupkumar
2002-01-01
We construct spectral triples for the C^*-algebra of continuous functions on the quantum SU(2) group and the quantum sphere. There has been various approaches towards building a calculus on quantum spaces, but there seems to be very few instances of computations outlined in chapter~6 of Connes' book. We give detailed computations of the associated Connes-de Rham complex and the space of L_2-forms.
Quantum entanglement in the one-dimensional spin-orbital SU (2 )⊗XXZ model
You, Wen-Long; Horsch, Peter; Oleś, Andrzej M.
2015-08-01
We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU (2 )⊗XXZ model with SU(2) spin exchange and anisotropic XXZ orbital exchange interactions and negative exchange coupling constant. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions, we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational-invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic SU (2 )⊗SU (2) limit. Surprisingly, for finite transverse orbital coupling, the long-range spin-singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover, we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore, we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly, one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size. We demonstrate that spin-orbital excitons can be experimentally explored using resonant inelastic x-ray scattering, where the strongly entangled exciton states can be easily distinguished from the spin-orbital continuum.
SU(4)-SU(2) crossover and spin-filter properties of a double quantum dot nanosystem
Lopes, V.; Padilla, R. A.; Martins, G. B.; Anda, E. V.
2017-06-01
The SU(4)-SU(2) crossover, driven by an external magnetic field h , is analyzed in a capacitively coupled double quantum dot device connected to independent leads. As one continuously charges the dots from empty to quarter filled, by varying the gate potential Vg, the crossover starts when the magnitude of the spin polarization of the double quantum dot, as measured by - , becomes finite. Although the external magnetic field breaks the SU(4) symmetry of the Hamiltonian, the ground state preserves it in a region of Vg, where - =0 . Once the spin polarization becomes finite, it initially increases slowly until a sudden change occurs, in which (polarization direction opposite to the magnetic field) reaches a maximum and then decreases to negligible values abruptly, at which point an orbital SU(2) ground state is fully established. This crossover from one Kondo state, with emergent SU(4) symmetry, where spin and orbital degrees of freedom all play a role, to another, with SU(2) symmetry, where only orbital degrees of freedom participate, is triggered by a competition between g μBh , the energy gain by the Zeeman-split polarized state and the Kondo temperature TKS U (4 ), the gain provided by the SU(4) unpolarized Kondo-singlet state. At fixed magnetic field, the knob that controls the crossover is the gate potential, which changes the quantum dots occupancies. If one characterizes the occurrence of the crossover by Vgmax, the value of Vg where reaches a maximum, one finds that the function f relating the Zeeman splitting, Bmax, which corresponds to Vgmax, i.e., Bmax=f (Vgmax) , has a similar universal behavior to that of the function relating the Kondo temperature to Vg. In addition, our numerical results show that near the SU(4) Kondo temperature and for relatively small magnetic fields the device has a ground state that restricts the electronic population at the dots to be spin polarized along the magnetic field. These two facts introduce very efficient spin
Finite temperature quantum correlations in su(2)(c) quark states and quantum spin models
Hamieh, S; Tawfik, A
The entanglement at finite temperatures is analyzed by using thermal models for colored quarks making tip the hadron physical states. We have found that these quantum correlations entirely vanish at T-c >= m(q)/ln(1.5). For temperatures larger than T-c the correlations are classical. We have also
Energy Technology Data Exchange (ETDEWEB)
Shnirman, A., E-mail: alexander.shnirman@kit.edu [Karlsruhe Institute of Technology, Institut fur Theorie der Kondensierten Materie (Germany); Saha, A. [Institute of Physics (India); Burmistrov, I. S. [Russian Academy of Sciences, Landau Institute for Theoretical Physics (Russian Federation); Kiselev, M. N. [International Center for Theoretical Physics (Italy); Altland, A. [Universität zu Köln, Institut für Theoretische Physik (Germany); Gefen, Y. [Weizmann Institute of Science, Department of Condensed Matter Physics (Israel)
2016-03-15
There are two paradigmatic frameworks for treating quantum systems coupled to a dissipative environment: the Caldeira–Leggett and Ambegaokar–Eckern–Schön approaches. Here, we recall the differences between them and explain the consequences of applying each to a zero-dimensional spin (having an SU(2) symmetry) in a dissipative environment (a dissipative quantum dot near or beyond the Stoner instability point).
Two-Dimensional Exactly Solvable Quantum Model Obtained from SU(3)/SU(2) Homogenous Space
Panahi, H.; Nemati, M.
2017-07-01
In this paper by using of the Euler-angle parametrization of SU(3) Lie group and its symmetry space on S 5≅ S U(3) / S U(2), we obtain one two-dimensional Hamiltonian defined on S 2sphere. We show that the quantum system can be interpreted as the motion of a charged particle in presence of an external electric field. We solve the model and obtain its spectrum.
Drinfeld Doubles for Finite Subgroups of SU(2 and SU(3 Lie Groups
Directory of Open Access Journals (Sweden)
Robert Coquereaux
2013-05-01
Full Text Available Drinfeld doubles of finite subgroups of SU(2 and SU(3 are investigated in detail. Their modular data – S, T and fusion matrices – are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain identities on these tensor product or fusion multiplicities under conjugation of representations that had been discussed in our recent paper [J. Phys. A: Math. Theor. 44 (2011, 295208, 26 pages], proved to hold for simple and affine Lie algebras, and found to be generally wrong for finite groups. It is shown here that these identities fail also in general for Drinfeld doubles, indicating that modularity of the fusion category is not the decisive feature. Along the way, we collect many data on these Drinfeld doubles which are interesting for their own sake and maybe also in a relation with the theory of orbifolds in conformal field theory.
Indian Academy of Sciences (India)
Jyotishman Bhowmick
2015-11-07
Nov 7, 2015 ... NONcommutative spaces. 2. Banica and Bichon defined quantum symmetry groups for finite metric spaces, finite graphs, etc. 3. Lots of examples computed leading to discovery of completely new kinds of quantum groups. Jyotishman Bhowmick (Indian Statistical Institute). Quantum isometry groups. 07.11.
Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies
Hofmann, Ralf
2013-01-01
A brief review of effective SU(2) Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field $\\phi$, based on non-propagating (anti)selfdual field configurations of topological charge unity. We explain why the screening physics of an SU(2) photon is subject to an electric-magnetically dual interpretation. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB) determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2) Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2) photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planc...
Thermodynamics of SU(2 quantum Yang-Mills theory and CMB anomalies
Directory of Open Access Journals (Sweden)
Hofmann Ralf
2014-04-01
Full Text Available A brief review of effective SU(2 Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field φ, based on non-propagating (antiselfdual field configurations of topological charge unity. We also discuss kinematic constraints on interacting propagating gauge fields implied by the according spatial coarse-graining, and we explain why the screening physics of an SU(2 photon is subject to an electric-magnetically dual interpretation. This argument relies on the fact that only (anticalorons of scale parameter ρ ∼ |φ|−1 contribute to the coarse-graining required for thermal-ground-state emergence at temperature T. Thus, use of the effective gauge coupling e in the (anticaloron action is justified, yielding the value ħ for the latter at almost all temperatures. As a consequence, the indeterministic transition of initial to final plane waves caused by an effective, pointlike vertex is fundamentally mediated in Euclidean time by a single (anticaloron being part of the thermal ground state. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2 Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2 photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planck collaboration. Finally, six relativistic polarisations residing in the SU(2 vector modes roughly match the number of degrees of freedom in cosmic neutrinos (Planck which would disqualify the latter as radiation. Indeed, if interpreted as single center
Goswami, Debashish
2016-01-01
This book offers an up-to-date overview of the recently proposed theory of quantum isometry groups. Written by the founders, it is the first book to present the research on the “quantum isometry group”, highlighting the interaction of noncommutative geometry and quantum groups, which is a noncommutative generalization of the notion of group of isometry of a classical Riemannian manifold. The motivation for this generalization is the importance of isometry groups in both mathematics and physics. The framework consists of Alain Connes’ “noncommutative geometry” and the operator-algebraic theory of “quantum groups”. The authors prove the existence of quantum isometry group for noncommutative manifolds given by spectral triples under mild conditions and discuss a number of methods for computing them. One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitl...
Reducibility of quantum representations of mapping class groups
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Fjelstad, Jens
2010-01-01
that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture...... this decomposition is a complete decomposition into irreducible representations for high enough levels....
SU(2 Yang–Mills Theory: Waves, Particles, and Quantum Thermodynamics
Directory of Open Access Journals (Sweden)
Ralf Hofmann
2016-08-01
Full Text Available We elucidate how Quantum Thermodynamics at temperature T emerges from pure and classical S U ( 2 Yang–Mills theory on a four-dimensional Euclidean spacetime slice S 1 × R 3 . The concept of a (deconfining thermal ground state, composed of certain solutions to the fundamental, classical Yang–Mills equation, allows for a unified addressation of both (classical wave- and (quantum particle-like excitations thereof. More definitely, the thermal ground state represents the interplay between nonpropagating, periodic configurations which are electric-magnetically (antiselfdual in a non-trivial way and possess topological charge modulus unity. Their trivial-holonomy versions—Harrington–Shepard (HS (anticalorons—yield an accurate a priori estimate of the thermal ground state in terms of spatially coarse-grained centers, each containing one quantum of action ℏ localized at its inmost spacetime point, which induce an inert adjoint scalar field ϕ ( | ϕ | spatio-temporally constant. The field ϕ , in turn, implies an effective pure-gauge configuration, a μ gs , accurately describing HS (anticaloron overlap. Spatial homogeneity of the thermal ground-state estimate ϕ , a μ gs demands that (anticaloron centers are densely packed, thus representing a collective departure from (antiselfduality. Effectively, such a “nervous” microscopic situation gives rise to two static phenomena: finite ground-state energy density ρ gs and pressure P gs with ρ gs = − P gs as well as the (adjoint Higgs mechanism. The peripheries of HS (anticalorons are static and resemble (antiselfdual dipole fields whose apparent dipole moments are determined by | ϕ | and T, protecting them against deformation potentially caused by overlap. Such a protection extends to the spatial density of HS (anticaloron centers. Thus the vacuum electric permittivity ϵ 0 and magnetic permeability μ 0 , supporting the propagation of wave-like disturbances in the U ( 1 Cartan
Energy Technology Data Exchange (ETDEWEB)
Pressley, A.; Chari, V. (King' s Coll., London (UK). Dept. of Mathematics Tata Inst. of Fundamental Research, Bombay (India). School of Mathematics)
1990-12-01
The authors presents an introduction to quantum groups defined as a deformation of the universal enveloping algebra of a Lie algebra. After the description of Hopf algebras with some examples the approach of Drinfel'd and Jimbo is described, where the quantization of a Lie algebra represents a Hopf algebra, defined over the algebra of formal power series in an indetermined h. The authors show that this approach arises from a r-matrix, which satisfies the classical Yang-Baxter equation. As example quantum sl{sub 2} is considered. Furthermore the approaches of Manin and Woroniwicz and the R-matrix approach are described. (HSI).
Directory of Open Access Journals (Sweden)
Ralf Hofmann
2017-10-01
Full Text Available Based on a recent numerical simulation of the temporal evolution of a spherically perturbed BPS monopole, SU(2 Yang-Mills thermodynamics, Louis de Broglie’s deliberations on the disparate Lorentz transformations of the frequency of an internal “clock” on one hand and the associated quantum energy on the other hand, and postulating that the electron is represented by a figure-eight shaped, self-intersecting center vortex loop in SU(2 Quantum Yang-Mills theory we estimate the spatial radius R 0 of this self-intersection region in terms of the electron’s Compton wave length λ C . This region, which is immersed into the confining phase, constitutes a blob of deconfining phase of temperature T 0 mildly above the critical temperature T c carrying a frequently perturbed BPS monopole (with a magnetic-electric dual interpretation of its charge w.r.t. U(1⊂SU(2. We also establish a quantitative relation between rest mass m 0 of the electron and SU(2 Yang-Mills scale Λ , which in turn is defined via T c . Surprisingly, R 0 turns out to be comparable to the Bohr radius while the core size of the monopole matches λ C , and the correction to the mass of the electron due to Coulomb energy is about 2%.
Quantum groups: Geometry and applications
Energy Technology Data Exchange (ETDEWEB)
Chu, Chong -Sun [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group; Univ. of California, Berkeley, CA (United States)
1996-05-13
The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge.
Pressley, Andrew
2002-02-01
To take stock and to discuss the most fruitful directions for future research, many of the world's leading figures met at the Durham Symposium on Quantum Groups in the summer of 1999, and this volume provides an excellent overview of the material presented there. It includes important surveys of both cyclotomic Hecke algebras and the dynamical Yang-Baxter equation. Plus contributions which treat the construction and classification of quantum groups or the associated solutions of the quantum Yang-Baxter equation. The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory of integrable systems.
Chari, Vyjayanthi; Pressley, Andrew N.
1995-10-01
Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. This book gives a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Researchers in mathematics and theoretical physics will enjoy this book.
Working group report: Quantum chromodynamics
Indian Academy of Sciences (India)
This is the report of the subgroup QCD of Working Group-4 at WHEPP-9. We present the activities that had taken place in the subgroup and report some of the partial results arrived at following the discussion at the working group meetings. Keywords. Quantum chromodynamics; resummation; extra dimensions; multi-leg.
Quantum Groups from Path Integrals
Freed, Daniel S.
1995-01-01
Lecture notes from the 1994 CRM-CAP Summer School ``Particles and Fields '94''. Covers material written elsewhere in a more leisurely fashion, including many exercises. Describes derivation of quantum groups from the Chern-Simons lagrangian for the case of a finite gauge group.
A group theoretic approach to quantum information
Hayashi, Masahito
2017-01-01
This textbook is the first one addressing quantum information from the viewpoint of group symmetry. Quantum systems have a group symmetrical structure. This structure enables to handle systematically quantum information processing. However, there is no other textbook focusing on group symmetry for quantum information although there exist many textbooks for group representation. After the mathematical preparation of quantum information, this book discusses quantum entanglement and its quantification by using group symmetry. Group symmetry drastically simplifies the calculation of several entanglement measures although their calculations are usually very difficult to handle. This book treats optimal information processes including quantum state estimation, quantum state cloning, estimation of group action and quantum channel etc. Usually it is very difficult to derive the optimal quantum information processes without asymptotic setting of these topics. However, group symmetry allows to derive these optimal solu...
Fusion Rings for Quantum Groups
DEFF Research Database (Denmark)
Andersen, Henning Haahr; Stroppel, Catharina
2014-01-01
We study the fusion rings of tilting modules for a quantum group at a root of unity modulo the tensor ideal of negligible tilting modules. We identify them in type A with the combinatorial rings from Korff, C., Stroppel, C.: The sl(ˆn)k-WZNW fusion ring: a combinato-rial construction and a realis......We study the fusion rings of tilting modules for a quantum group at a root of unity modulo the tensor ideal of negligible tilting modules. We identify them in type A with the combinatorial rings from Korff, C., Stroppel, C.: The sl(ˆn)k-WZNW fusion ring: a combinato-rial construction...... and a realisation as quotient of quantum cohomology. Adv. Math. 225(1), 200–268, (2010) and give a similar description of the sp2n-fusion ring in terms of non-commutative symmetric functions. Moreover we give a presentation of all fusion rings in classical types as quotients of polynomial rings. Finally we also...... compute the fusion rings for type G2....
Fixed point algebras for easy quantum groups
DEFF Research Database (Denmark)
Gabriel, Olivier; Weber, Moritz
2016-01-01
Compact matrix quantum groups act naturally on Cuntz algebras. The first author isolated certain conditions under which the fixed point algebras under this action are Kirchberg algebras. Hence they are completely determined by their K-groups. Building on prior work by the second author,we prove...... that free easy quantum groups satisfy these conditions and we compute the K-groups of their fixed point algebras in a general form. We then turn to examples such as the quantum permutation group S+ n,the free orthogonal quantum group O+ n and the quantum reflection groups Hs+ n. Our fixed point...
Directory of Open Access Journals (Sweden)
Guillermo García Fernández
2017-02-01
The result follows from strong antiscreening of the running coupling for those larger groups (with an appropriately small number of flavors together with scaling properties of the Dyson–Schwinger equation for the fermion mass.
Fusion Rings for Quantum Groups
DEFF Research Database (Denmark)
Andersen, Henning Haahr; Stroppel, Catharina
2012-01-01
We study the fusion rings of tilting modules for a quantum group at a root of unity modulo the tensor ideal of negligible tilting modules. We identify them in type A with the combinatorial rings from [12] and give a similar description of the sp2n-fusion ring in terms of noncommutative symmetric...... functions. Moreover we give a presentation of all fusion rings in classical types as quotients of polynomial rings. Finally we also compute the fu- sion rings for type G2....
Path integrals and coherent states of SU(2) and SU(1,1)
Inomata, Akira; Kuratsuji, Hiroshi
1992-01-01
The authors examine several topical subjects, commencing with a general introduction to path integrals in quantum mechanics and the group theoretical backgrounds for path integrals. Applications of harmonic analysis, polar coordinate formulation, various techniques and path integrals on SU(2) and SU(1, 1) are discussed. Soluble examples presented include particle-flux system, a pulsed oscillator, magnetic monopole, the Coulomb problem in curved space and others.The second part deals with the SU(2) coherent states and their applications. Construction and generalization of the SU(2) coherent sta
Quantum Groups, Property (T), and Weak Mixing
Brannan, Michael; Kerr, David
2017-11-01
For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having almost invariant vectors. This is a generalization of a theorem of Bekka and Valette from the group setting and was previously established in the case of low dual by Daws, Skalski, and Viselter. Our approach uses spectral techniques and is completely different from those of Bekka-Valette and Daws-Skalski-Viselter. By a separate argument we furthermore extend the result to second countable nonunimodular locally compact quantum groups, which are shown in particular not to have property (T), generalizing a theorem of Fima from the discrete setting. We also obtain quantum group versions of characterizations of property (T) of Kerr and Pichot in terms of the Baire category theory of weak mixing representations and of Connes and Weiss in terms of the prevalence of strongly ergodic actions.
From field theory to quantum groups
Jancewicz, B
1996-01-01
Professor Jerzy Lukierski, an outstanding specialist in the domain of quantum groups, will reach on May 21, 1995 the age of sixty. This is a birthday volume dedicated to him. It assumes the form of a collection of papers on a wide range of topics in modern research area from theoretical high energy physics to mathematical physics. Various topics of quantum groups will be treated with a special emphasis. Quantum groups is nowadays a very fashionable subject both in mathematics and high energy physics.
Note on quantum groups and integrable systems
Popolitov, A.
2016-01-01
The free-field formalism for quantum groups [preprint ITEP-M3/94, CRM-2202 hep-th/9409093] provides a special choice of coordinates on a quantum group. In these coordinates the construction of associated integrable system [arXiv:1207.1869] is especially simple. This choice also fits into general framework of cluster varieties [math.AG/0311245]—natural changes in coordinates are cluster mutations.
Braid group representation on quantum computation
Energy Technology Data Exchange (ETDEWEB)
Aziz, Ryan Kasyfil, E-mail: kasyfilryan@gmail.com [Department of Computational Sciences, Bandung Institute of Technology (Indonesia); Muchtadi-Alamsyah, Intan, E-mail: ntan@math.itb.ac.id [Algebra Research Group, Bandung Institute of Technology (Indonesia)
2015-09-30
There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.
Introduction to compact (matrix) quantum groups and Banica ...
Indian Academy of Sciences (India)
, India from 5–24 January 2015. We give basic definitions, properties and examples of compact quantum groups and compact matrix quantum groups such as the existence of a Haar state, the representation theory and Woronowicz's quantum ...
Working group report: Quantum chromodynamics
Indian Academy of Sciences (India)
The participants of the QCD working sub-group are: Rahul Basu, D Indumathi,. E Laenen, Swapan Majhi, Prakash Mathews, Anuradha Misra, Asmita Mukherjee,. R Ratabole, V Ravindran and W Vogelsang. The main focus of this working group had been to concentrate on some issues in resummation which are essential to ...
Quantum theory, groups and representations an introduction
Woit, Peter
2017-01-01
This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific ...
Quantum chromodynamics: Working group report
Indian Academy of Sciences (India)
This is the report of the QCD working group at WHEPP-6. Discussions and work on heavy ion collisions, polarized scattering, and collider phenomenology are reported. Keywords. QCD; polarized scattering; light front field theory; heavy ion physics; non-equilibrium field theory; parton distributions at LHC; fragmentation ...
Twisting Functors for Quantum Group Modules
DEFF Research Database (Denmark)
Pedersen, Dennis Hasselstrøm
We construct twisting functors for quantum group modules. First over the field Q(v) but later over any Z[v,v^{−1}]-algebra. The main results in this paper are a rigerous definition of these functors, a proof that they satisfy braid relations and applications to Verma modules.......We construct twisting functors for quantum group modules. First over the field Q(v) but later over any Z[v,v^{−1}]-algebra. The main results in this paper are a rigerous definition of these functors, a proof that they satisfy braid relations and applications to Verma modules....
Cryptanalysis of the Quantum Group Signature Protocols
Zhang, Ke-Jia; Sun, Ying; Song, Ting-Ting; Zuo, Hui-Juan
2013-11-01
Recently, the researches of quantum group signature (QGS) have attracted a lot of attentions and some typical protocols have been designed for e-payment system, e-government, e-business, etc. In this paper, we analyze the security of the quantum group signature with the example of two novel protocols. It can be seen that both of them cannot be implemented securely since the arbitrator cannot solve the disputes fairly. In order to show that, some possible attack strategies, which can be used by the malicious participants, are proposed. Moreover, the further discussions of QGS are presented finally, including some insecurity factors and improved ideas.
Working Group Report: Quantum Chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Campbell, J. M. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
2013-10-18
This is the summary report of the energy frontier QCD working group prepared for Snowmass 2013. We review the status of tools, both theoretical and experimental, for understanding the strong interactions at colliders. We attempt to prioritize important directions that future developments should take. Most of the efforts of the QCD working group concentrate on proton-proton colliders, at 14 TeV as planned for the next run of the LHC, and for 33 and 100 TeV, possible energies of the colliders that will be necessary to carry on the physics program started at 14 TeV. We also examine QCD predictions and measurements at lepton-lepton and lepton-hadron colliders, and in particular their ability to improve our knowledge of strong coupling constant and parton distribution functions.
SU(2|2) supersymmetric mechanics
Energy Technology Data Exchange (ETDEWEB)
Ivanov, Evgeny [Joint Institute for Nuclear Research,Dubna, Moscow Region, 141980 (Russian Federation); Lechtenfeld, Olaf [Institut für Theoretische Physik and Riemann Center for Geometry and Physics,Leibniz Universität Hannover,Appelstraße 2, 30167 Hannover (Germany); Sidorov, Stepan [Joint Institute for Nuclear Research,Dubna, Moscow Region, 141980 (Russian Federation)
2016-11-07
We introduce a new kind of non-relativistic N= 8 supersymmetric mechanics, associated with worldline realizations of the supergroup SU(2|2) treated as a deformation of flat N= 8, d=1 supersymmetry. Various worldline SU(2|2) superspaces are constructed as coset manifolds of this supergroup, and the corresponding superfield techniques are developed. For the off-shell SU(2|2) multiplets (3,8,5), (4,8,4) and (5,8,3), we construct and analyze the most general superfield and component actions. Common features are mass oscillator-type terms proportional to the deformation parameter and a trigonometric realization of the superconformal group OSp(4{sup ∗}|4) in the conformal cases. For the simplest (5,8,3) model the quantization is performed.
Infrared behaviors of SU(2 gauge theory
Directory of Open Access Journals (Sweden)
Tuominen Kimmo
2017-01-01
Full Text Available We will discuss some recent results in the determination of the location of the conformal window in SU(2 gauge theory with Nf fermions in the fundamental representation of the gauge group. In particular, we will demonstrate that the long distance behavior of the continuum theory with Nf = 6 is governed by an infrared stable fixed point.
A group signature scheme based on quantum teleportation
Wen, Xiaojun; Tian, Yuan; Ji, Liping; Niu, Xiamu
2010-05-01
In this paper, we present a group signature scheme using quantum teleportation. Different from classical group signature and current quantum signature schemes, which could only deliver either group signature or unconditional security, our scheme guarantees both by adopting quantum key preparation, quantum encryption algorithm and quantum teleportation. Security analysis proved that our scheme has the characteristics of group signature, non-counterfeit, non-disavowal, blindness and traceability. Our quantum group signature scheme has a foreseeable application in the e-payment system, e-government, e-business, etc.
Isometric coactions of compact quantum groups on compact ...
Indian Academy of Sciences (India)
We propose a notion of isometric coaction of a compact quantum group on a compact quantum metric space in the framework of Rieffel, where the metric structure is given by a Lipnorm. Within this setting we study the problem of the existence of a quantum isometry group.
Quantum gravity as a group field theory: a sketch
Oriti, Daniele
2005-01-01
We give a very brief introduction to the group field theory approach to quantum gravity, a generalisation of matrix models for 2-dimensional quantum gravity to higher dimension, that has emerged recently from research in spin foam models.
A correction to the Immirzi parameter of SU(2 spin networks
Directory of Open Access Journals (Sweden)
M. Sadiq
2015-02-01
Full Text Available The elegant predictions of loop quantum gravity are obscured by the free Immirzi parameter (γ. Dreyer (2003, considering the asymptotic quasinormal modes spectrum of a black hole, proposed that γ may be fixed by letting the j=1 transitions of spin networks as the dominant processes contributing to the black hole area, as opposed to the expected j=1/2 transitions. This suggested that the gauge group of the theory might be SO(3 rather than SU(2. Corichi (2003, maintaining SU(2 as the underlying gauge group, and invoking the principle of local fermion-number conservation, reported the same value of γ for j=1 processes as obtained by Dreyer. In this note, preserving the SU(2 structure of the theory, and considering j=1 transitions as the dominant processes, we point out that the value of γ is in fact twice the value reported by these authors. We arrive at this result by assuming the asymptotic quasinormal modes themselves as dynamical systems obeying SU(2 symmetry.
General Covariance from the Quantum Renormalization Group
Shyam, Vasudev
2016-01-01
The Quantum renormalization group (QRG) is a realisation of holography through a coarse graining prescription that maps the beta functions of a quantum field theory thought to live on the `boundary' of some space to holographic actions in the `bulk' of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the $D + 1$ dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the $D$ dimensional boundary. This will be a particular form of the Wess--Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Po...
Winter School on Operator Spaces, Noncommutative Probability and Quantum Groups
2017-01-01
Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems. A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions. The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The l...
An E-payment system based on quantum group signature
Xiaojun, Wen
2010-12-01
Security and anonymity are essential to E-payment systems. However, existing E-payment systems will easily be broken into soon with the emergence of quantum computers. In this paper, we propose an E-payment system based on quantum group signature. In contrast to classical E-payment systems, our quantum E-payment system can protect not only the users' anonymity but also the inner structure of customer groups. Because of adopting the two techniques of quantum key distribution, a one-time pad and quantum group signature, unconditional security of our E-payment system is guaranteed.
A secure quantum group signature scheme based on Bell states
Zhang, Kejia; Song, Tingting; Zuo, Huijuan; Zhang, Weiwei
2013-04-01
In this paper, we propose a new secure quantum group signature with Bell states, which may have applications in e-payment system, e-government, e-business, etc. Compared with the recent quantum group signature protocols, our scheme is focused on the most general situation in practice, i.e. only the arbitrator is trusted and no intermediate information needs to be stored in the signing phase to ensure the security. Furthermore, our scheme has achieved all the characteristics of group signature—anonymity, verifiability, traceability, unforgetability and undeniability, by using some current developed quantum and classical technologies. Finally, a feasible security analysis model for quantum group signature is presented.
Working group report: Quantum chromodynamics (QCD) and ...
Indian Academy of Sciences (India)
Quantum chromodynamics; perturbative; non-perturbative; quark gluon plasma. PACS No. 12.38.-t. 1. Introduction. Quantum chromodynamics (QCD), the theory of strong interaction physics has been well established both theoretically .... are removed by the redefinition of parton densities at some arbitrary factorization scale.
25 Years of Quantum Groups: from Definition to Classification
Directory of Open Access Journals (Sweden)
A. Stolin
2008-01-01
Full Text Available In mathematics and theoretical physics, quantum groups are certain non-commutative, non-cocommutative Hopf algebras, which first appeared in the theory of quantum integrable models and later they were formalized by Drinfeld and Jimbo. In this paper we present a classification scheme for quantum groups, whose classical limit is a polynomial Lie algebra. As a consequence we obtain deformed XXX and XXZ Hamiltonians.
Functional renormalization group methods in quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Braun, J.
2006-12-18
We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)
PREFACE Quantum Groups, Quantum Foundations and Quantum Information: a Festschrift for Tony Sudbery
Weigert, Stefan
2010-11-01
On 29 July 2008, Professor Anthony Thomas Sudbery - known as Tony to his friends and colleagues - celebrated his 65th birthday. To mark this occasion and to honour Tony's scientific achievements, a 2-day Symposion was held at the University of York on 29-30 September 2008 under the sponsorship of the Institute of Physics and the London Mathematical Society. The breadth of Tony's research interests was reflected in the twelve invited lectures by A Beige, I Bengtsson, K Brown, N Cerf, E Corrigan, J Ladyman, A J Macfarlane, S Majid, C Manogue, S Popescu, J Ryan and R W Tucker. This Festschrift, also made possible by the generosity of the IOP and the LMS, reproduces the majority of these contributions together with other invited papers. Tony obtained his PhD from the University of Cambridge in 1970. His thesis, written under the guidance of Alan Macfarlane, is entitled Some aspects of chiral su(3) × su(3) symmetry in hadron dynamics. He arrived in York in 1971 with his wife Rodie, two young daughters, a lively mind and a very contemporary shock of hair. He was at that stage interested in mathematical physics and so was classed as an applied mathematician in the departmental division in place at that time. But luckily Tony did not fit into this category. His curiosity is combined with a good nose for problems and his capacity for knocking off conjectures impressed us all. Within a short time of his arrival he was writing papers on group theory, complex analysis and combinatorics, while continuing to work on quantum mechanics. His important paper on quaternionic analysis is an example of the imagination and elegance of his ideas. By developing a derivative, he replaced the relatively obscure analytical theory of quaternions by one informed by modern complex analysis. Other interests emerged, centred round the quantum: quantum mechanics and its foundations, quantum groups and quantum information. He didn't just dabble in these areas but mastered them, gaining a national
Isometric coactions of compact quantum groups on compact ...
Indian Academy of Sciences (India)
isometry group' in Rieffel's framework, we might expect it to be compact. Therefore, we gather some information on compact quantum groups and compact quantum metric spaces together with other preliminary notions in the second section. Next, we introduce our notion of isometric coactions in the third section. We show in ...
Energy Technology Data Exchange (ETDEWEB)
Enríquez, Marco; Rosas-Ortiz, Oscar, E-mail: orosas@fis.cinvestav.mx
2013-12-15
We review the properties of the Kronecker (direct, or tensor) product of square matrices A⊗B⊗C⋯ in terms of Hubbard operators. In its simplest form, a Hubbard operator X{sub n}{sup i,j} can be expressed as the n-square matrix which has entry 1 in position (i,j) and zero in all other entries. The algebra and group properties of the observables that define a multipartite quantum system are notably straightforward in such a framework. In particular, we use the Kronecker product in Hubbard notation to get the Clebsch–Gordan decomposition of the product group SU(2)×SU(2). Finally, the n-dimensional irreducible representations so obtained are used to derive closed forms of the Clebsch–Gordan coefficients that rule the addition of angular momenta. Our results can be further developed in many different directions. -- Highlights: •The Kronecker product is studied in terms of Hubbard operators. •Complicated calculations involving large matrices are reduced to simple relations of subscripts. •The algebraic properties of the quantum observables of multipartite systems are studied. •The Clebsch–Gordan coefficients are given in terms of hypergeometric {sub 3}F{sub 2} functions. •The results can be further developed in many different directions.
Energy Technology Data Exchange (ETDEWEB)
Wu, Wei [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China); Beijing Computational Science Research Center, Beijing 100193 (China); Xu, Jing-Bo, E-mail: xujb@zju.edu.cn [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China)
2017-01-30
We investigate the performances of quantum coherence and multipartite entanglement close to the quantum critical point of a one-dimensional anisotropic spin-1/2 XXZ spin chain by employing the real-space quantum renormalization group approach. It is shown that the quantum criticality of XXZ spin chain can be revealed by the singular behaviors of the first derivatives of renormalized quantum coherence and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized quantum coherence and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical point of XXZ spin chain. - Highlights: • The QPT of XXZ chain is studied by renormalization group. • The renormalized coherence and multiparticle entanglement is investigated. • Scaling laws of renormalized coherence and multiparticle entanglement are revealed.
Quantum group symmetry of classical and noncommutative geometry
Indian Academy of Sciences (India)
Debashish Goswami
2016-07-01
Jul 1, 2016 ... metric spaces. Open problems. Quantum groups coming from deformation. A favourite procedure to obtain model of quantum physics: some sort of deformation (Rieffel-deformation, cocycle twists etc. more general algebraic deformations...) of classical phase-space. Drinfeld and Jimbo constructed many ...
Quantum group symmetry and q-tensor algebras
Biedenharn, Lawrence Christian
1995-01-01
Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations
Structure of irreducibly covariant quantum channels for finite groups
Mozrzymas, Marek; Studziński, Michał; Datta, Nilanjana
2017-05-01
We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation (U) of a finite group (G), whenever U ⊗Uc is simply reducible (with Uc being the contragradient representation). Using the theory of group representations, we obtain the spectral decomposition of any such linear map. The eigenvalues and orthogonal projections arising in this decomposition are expressed entirely in terms of representation characteristics of the group G. This in turn yields necessary and sufficient conditions on the eigenvalues of any such linear map for it to be a quantum channel. We also obtain a wide class of quantum channels which are irreducibly covariant by construction. For two-dimensional irrreducible representations of the symmetric group S(3), and the quaternion group Q, we also characterize quantum channels which are both irreducibly covariant and entanglement breaking.
Quantum Walks, Weyl Equation and the Lorentz Group
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-08-01
Quantum cellular automata and quantum walks provide a framework for the foundations of quantum field theory, since the equations of motion of free relativistic quantum fields can be derived as the small wave-vector limit of quantum automata and walks starting from very general principles. The intrinsic discreteness of this framework is reconciled with the continuous Lorentz symmetry by reformulating the notion of inertial reference frame in terms of the constants of motion of the quantum walk dynamics. In particular, among the symmetries of the quantum walk which recovers the Weyl equation—the so called Weyl walk—one finds a non linear realisation of the Poincaré group, which recovers the usual linear representation in the small wave-vector limit. In this paper we characterise the full symmetry group of the Weyl walk which is shown to be a non linear realization of a group which is the semidirect product of the Poincaré group and the group of dilations.
Faithful actions of locally compact quantum groups on classical spaces
Goswami, Debashish; Roy, Sutanu
2017-07-01
We construct examples of locally compact quantum groups coming from bicrossed product construction, including non-Kac ones, which can faithfully and ergodically act on connected classical (noncompact) smooth manifolds. However, none of these actions can be isometric in the sense of Goswami (Commun Math Phys 285(1):141-160, 2009), leading to the conjecture that the result obtained by Goswami and Joardar (Rigidity of action of compact quantum groups on compact, connected manifolds, 2013. arXiv:1309.1294) about nonexistence of genuine quantum isometry of classical compact connected Riemannian manifolds may hold in the noncompact case as well.
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2013-07-19
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
Energy Technology Data Exchange (ETDEWEB)
Vernek, E. [Instituto de Física, Universidade Federal de Uberlândia, Uberlândia, MG 38400-902 (Brazil); Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos-SP 13560-970 (Brazil); Büsser, C. A. [Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, D-80333 München (Germany); Anda, E. V. [Departamento de Física, Pontifícia Universidade Católica, Rio de Janeiro-RJ (Brazil); Feiguin, A. E. [Department of Physics, Northeastern University, Boston, Massachusetts 02115 (United States); Martins, G. B., E-mail: martins@oakland.edu [Department of Physics, Oakland University, Rochester, Michigan 48309 (United States); Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)
2014-03-31
A double quantum dot device, connected to two channels that only interact through interdot Coulomb repulsion, is analyzed using the numerical renormalization group technique. Using a two-impurity Anderson model, and realistic parameter values [S. Amasha, A. J. Keller, I. G. Rau, A. Carmi, J. A. Katine, H. Shtrikman, Y. Oreg, and D. Goldhaber-Gordon, Phys. Rev. Lett. 110, 046604 (2013)], it is shown that, by applying a moderate magnetic field and independently adjusting the gate potential of each quantum dot at half-filling, a spin-orbital SU(2) Kondo state can be achieved where the Kondo resonance originates from spatially separated parts of the device. Our results clearly link this spatial separation effect to currents with opposing spin polarizations in each channel, i.e., the device acts as a spin filter. In addition, an experimental probe of this polarization effect is suggested, pointing to the exciting possibility of experimentally probing the internal structure of an SU(2) Kondo state.
Temme, F P
2004-03-01
The physics of dual group scalar invariants (SIs) as (Lie algebraic) group measures (L-GMs) and its significance to non-Abelian NMR spin systems motivates this overview of uniform general-2n [AX](2n) spin evolution, which represents an extensive addendum to Corio's earlier (essentially restricted) view of Abelian spin system SU(2)-based SI-cardinalities. The [Formula: see text] values in [J. Magn. Reson., 134 (1998) 131] arise from strictly linear recoupled time-reversal invariance (TRI) models. In contrast, here we discuss the physical significance of an alternative polyhedral combinatorics approach to democratic recoupling (DR), a property inherent in both the TRI and statistical sampling. Recognition of spin ensemble SIs as being L-GMs over isomorphic algebras is invaluable in many DR-based NMR problems. Various [AX]n model spin systems, including the [AX]3 bis odd-odd parity spin system, are examined as direct applications of these L-GM- and combinatorial-based SI ideas. Hence in place of /SI/=15 (implied by Corio's [Formula: see text] approach), the bis 3-fold spin system cardinality is seen now as constrained to a single invariant on an isomorphic product algebra under L-GMs, in accord with the subspectral analysis of Jones et al. [Canad. J. Chem., 43 (1965) 683]. The group projective ideas cited here for DR (as cf. to graph theoretic views) apply to highly degenerate non-Abelian problems. Over dual tensorial bases, they define models of spin dynamical evolution whose (SR) quasiparticle superboson carrier (sub)spaces are characterised by SIs acting as explicit auxiliary labels [Physica, A198 (1993) 245; J. Math. Chem., 31 (2002) 281]. A deeper [Formula: see text] network-based view of spin-alone space developed in Balasubramanian's work [J. Chem. Phys., 78 (1983) 6358] is especially important, (e.g.) in the study of spin waves [J. Math. Chem., 31 (2002) 363]. Beyond the specific NMR SIs derived here, there are DR applications where a sporadic, still higher, 2
Perturbative dynamics of open quantum systems by renormalization group method
Kukita, Shingo
2017-10-01
We analyze perturbative dynamics of a composite system consisting of a quantum mechanical system and an environment by the renormalization group (RG) method. The solution obtained from the RG method has no secular terms and approximates the exact solution for a long time interval. Moreover, the RG method causes a reduction of the dynamics of the composite system under some assumptions. We show that this reduced dynamics is closely related to a quantum master equation for the quantum mechanical system. We compare this dynamics with the exact dynamics in an exactly solvable spin-boson model.
Working group report: Quantum chromodynamics sub-group
Indian Academy of Sciences (India)
group. Coordinator: ASMITA MUKHERJEE7,∗. Working group members: R Basu1, H Dahiya2, L Gamberg3, R Godbole10,. S Gupta4, M C Kumar5, L Magnea6, P Mathews5, N Mathur4, A Mukherjee7,. P J Mulders8, V Ravindran9 and A Tripathi9.
Diffeomorphism Group Representations in Relativistic Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Goldin, Gerald A. [Rutgers Univ., Piscataway, NJ (United States); Sharp, David H. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-20
We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.
SU(2) Flat Connection on Riemann Surface and Twisted Geometry with Cosmological Constant
Han, Muxin
2016-01-01
SU(2) flat connection on 2D Riemann surface is shown to relate to the generalized twisted geometry in 3D space with cosmological constant. Various flat connection quantities on Riemann surface are mapped to the geometrical quantities in discrete 3D space. We propose that the moduli space of SU(2) flat connections on Riemann surface generalizes the phase space of twisted geometry or Loop Quantum Gravity to include the cosmological constant.
Multi-group dynamic quantum secret sharing with single photons
Energy Technology Data Exchange (ETDEWEB)
Liu, Hongwei [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Ma, Haiqiang, E-mail: hqma@bupt.edu.cn [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Wei, Kejin [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Yang, Xiuqing [School of Science, Beijing Jiaotong University, Beijing 100044 (China); Qu, Wenxiu; Dou, Tianqi; Chen, Yitian; Li, Ruixue; Zhu, Wu [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China)
2016-07-15
In this letter, we propose a novel scheme for the realization of single-photon dynamic quantum secret sharing between a boss and three dynamic agent groups. In our system, the boss can not only choose one of these three groups to share the secret with, but also can share two sets of independent keys with two groups without redistribution. Furthermore, the security of communication is enhanced by using a control mode. Compared with previous schemes, our scheme is more flexible and will contribute to a practical application. - Highlights: • A multi-group dynamic quantum secret sharing with single photons scheme is proposed. • Any one of the groups can be chosen to share secret through controlling the polarization of photons. • Two sets of keys can be shared simultaneously without redistribution.
General Impossibility of Group Homomorphic Encryption in the Quantum World
Armknecht, Frederik; Gagliardoni, Tommaso; Katzenbeisser, Stefan; Peter, Andreas
2014-01-01
Group homomorphic encryption represents one of the most important building blocks in modern cryptography. It forms the basis of widely-used, more sophisticated primitives, such as CCA2-secure encryption or secure multiparty computation. Unfortunately, recent advances in quantum computation show that
Introduction to compact (matrix) quantum groups and Banica ...
Indian Academy of Sciences (India)
Moritz Weber
2017-11-27
Nov 27, 2017 ... Introduction. The study of symmetries in mathematics is almost as old as mathematics itself. From the 19th century onwards, symmetries are mostly modelled by ... In the second half, we give an introduction to Banica–Speicher quantum groups [31], .... Philosophy behind non-commutative function algebras.
Differential geometry on Hopf algebras and quantum groups
Energy Technology Data Exchange (ETDEWEB)
Watts, Paul [Univ. of California, Berkeley, CA (United States)
1994-12-15
The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and used to define and discuss quantum Lie algebras and their properties. The Cartan calculus of the exterior derivative, Lie derivative, and inner derivation is found for both the universal and general differential calculi of an arbitrary Hopf algebra, and, by restricting to the quasitriangular case and using the numerical R-matrix formalism, the aforementioned structures for quantum groups are determined.
Renormalization group and continuum limit of quantum cellular automata
Energy Technology Data Exchange (ETDEWEB)
Zimboras, Zoltan [Quantum Information Theory Group, ISI, Torino (Italy)
2012-07-01
We develop a renormalization group formalism for quantum cellular automata (reminiscent of the algebraic renormalization group of Buchholz and Verch). Using this formalism, we can define the continuum limit for certain automata. As a particular example, we show that the continuum limit of the so-called ''Glider Clifford cellular automaton'' is the 1+1 dimensional relativistic QFT of free Majorana fermions.
Some prime factorization results for free quantum group factors
Isono, Yusuke
2014-01-01
We prove some unique factorization results for tensor products of free quantum group factors. They are type III analogues of factorization results for direct products of bi-exact groups established by Ozawa and Popa. In the proof, we first take continuous cores of the tensor products, which satisfy a condition similar to condition (AO), and discuss some factorization properties for the continuous cores. We then deduce factorization properties for the original type III factors. We also prove s...
Energy Technology Data Exchange (ETDEWEB)
Xiao, Hailin [Wenzhou University, College of Physics and Electronic Information Engineering, Wenzhou (China); Southeast University, National Mobile Communications Research Laboratory, Nanjing (China); Guilin University of Electronic Technology, Ministry of Education, Key Laboratory of Cognitive Radio and Information Processing, Guilin (China); Zhang, Zhongshan [University of Science and Technology Beijing, Beijing Engineering and Technology Research Center for Convergence Networks and Ubiquitous Services, Beijing (China); Chronopoulos, Anthony Theodore [University of Texas at San Antonio, Department of Computer Science, San Antonio, TX (United States)
2017-10-15
In quantum computing, nice error bases as generalization of the Pauli basis were introduced by Knill. These bases are known to be projective representations of finite groups. In this paper, we propose a group representation approach to the study of quantum stabilizer codes. We utilize this approach to define decoherence-free subspaces (DFSs). Unlike previous studies of DFSs, this type of DFSs does not involve any spatial symmetry assumptions on the system-environment interaction. Thus, it can be used to construct quantum error-avoiding codes (QEACs) that are fault tolerant automatically. We also propose a new simple construction of QEACs and subsequently develop several classes of QEACs. Finally, we present numerical simulation results encoding the logical error rate over physical error rate on the fidelity performance of these QEACs. Our study demonstrates that DFSs-based QEACs are capable of providing a generalized and unified framework for error-avoiding methods. (orig.)
Xiao, Hailin; Zhang, Zhongshan; Chronopoulos, Anthony Theodore
2017-10-01
In quantum computing, nice error bases as generalization of the Pauli basis were introduced by Knill. These bases are known to be projective representations of finite groups. In this paper, we propose a group representation approach to the study of quantum stabilizer codes. We utilize this approach to define decoherence-free subspaces (DFSs). Unlike previous studies of DFSs, this type of DFSs does not involve any spatial symmetry assumptions on the system-environment interaction. Thus, it can be used to construct quantum error-avoiding codes (QEACs) that are fault tolerant automatically. We also propose a new simple construction of QEACs and subsequently develop several classes of QEACs. Finally, we present numerical simulation results encoding the logical error rate over physical error rate on the fidelity performance of these QEACs. Our study demonstrates that DFSs-based QEACs are capable of providing a generalized and unified framework for error-avoiding methods.
Numerical Results for SU(4) and SU(2) Kondo Effect in Carbon Nanotubes
Martins, George; Busser, Carlos
2006-03-01
New numerical results are presented for the Kondo effect in Carbon Nanotube (CNT) quantum dots (QDs). As recently reported by P. Jarillo-Herrero et al. (Nature 434, 484 (2005)), the Kondo effect in CNTs presents an SU(4) symmetry, which arises from the entanglement of orbital and spin degrees of freedom. As the number of co-tunneling processes increases, thanks to the extra (orbital) degree of freedom, the Kondo temperature reaches a high value of TK=7.7K. Interesting considerations can be drawn regarding the change from SU(4) to SU(2) symmetries depending on the hopping matrix elements between the leads and the CNT QD. Our results will analyze the transition between the SU(4) and the so-called two-level SU(2) (2LSU(2)) Kondo regimes induced by the variation of the coupling of the QD to the leads. The effect of an external magnetic field along the tube direction will also be analyzed. Our results will be compared with available Numerical Renormalization Group (NRG) results by M-S Choi et al. (Phys. Rev. Lett. 95, 067204 (2005)). A comparison with the experimental results will be made to gauge the adequacy of the model and approximations made.
Fundamental representations of quantum groups at roots of 1
Chari, Vyjayanthi; Pressley, Andrew
1992-10-01
To every finite-dimensional irreducible representation V of the quantum group Uɛ( g) where ɛ is a primitive lth root of unity ( l odd) and g is a finite-dimensional complex simple Lie algebra, de Concini, Kac and Procesi have associated a conjugacy class C V in the adjoint group G of g. We describe explicitly, when g is of type A n , B n , C n , or D n , the representations associated to the conjugacy classes of minimal positive dimension. We call such representations fundamental and prove that, for any conjugacy class, there is an associated representation which is contained in a tensor product of fundamental representations.
Quasi-Hopf twistors for elliptic quantum groups
Jimbo, M; Odake, S; Shiraishi, J
1997-01-01
The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al., Felder). Fronsdal made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum affine algebra U_q(g). In this paper we present an explicit formula for the twistors in the form of an infinite product of the universal R matrix of U_q(g). We also prove the shifted cocycle condition for the twistors, thereby completing Fronsdal's findings. This construction entails that, for generic values of the deformation parameters, representation theory for U_q(g) carries over to the elliptic algebras, including such objects as evaluation modules, highest weight modules and vertex operators. In particular, we confirm the conjectures of Foda et al. concerning the elliptic algebra A_{q,p}(^sl_2).
A novel quantum group signature scheme without using entangled states
Xu, Guang-Bao; Zhang, Ke-Jia
2015-07-01
In this paper, we propose a novel quantum group signature scheme. It can make the signer sign a message on behalf of the group without the help of group manager (the arbitrator), which is different from the previous schemes. In addition, a signature can be verified again when its signer disavows she has ever generated it. We analyze the validity and the security of the proposed signature scheme. Moreover, we discuss the advantages and the disadvantages of the new scheme and the existing ones. The results show that our scheme satisfies all the characteristics of a group signature and has more advantages than the previous ones. Like its classic counterpart, our scheme can be used in many application scenarios, such as e-government and e-business.
Quantum renormalization group for ground-state fidelity
Langari, A.; Rezakhani, A. T.
2012-05-01
Ground-state fidelity (GSF) and quantum renormalization group (QRG) theory have proven to be useful tools in the study of quantum critical systems. Here we lay out a general, unified formalism of GSF and QRG; specifically, we propose a method for calculating GSF through QRG, obviating the need for calculating or approximating ground states. This method thus enhances the characterization of quantum criticality as well as scaling analysis of relevant properties with system size. We illustrate the formalism in the one-dimensional Ising model in a transverse field (ITF) and the anisotropic spin-1/2 Heisenberg (XXZ) model. Explicitly, we find the scaling behavior of the GSF for the ITF model in both small- and large-size limits, the corresponding critical exponents, the exact value of the GSF in the thermodynamic limit and a closed form for the GSF for arbitrary size and system parameters. In the case of the XXZ model, we also present an analytic expression for the GSF, which captures well the criticality of the model, hence excluding doubts that GSF might be an insufficient tool for signaling criticality in this model.
Affine group representation formalism for four dimensional, Lorentzian, quantum gravity
Ching-Yi, Chou; Soo, Chopin
2012-01-01
The Hamiltonian constraint of 4-dimensional General Relativity is recast explicitly in terms of the Chern--Simons functional and the local volume operator. In conjunction with the algebraic quantization program, application of the affine quantization concept due to Klauder facilitates the construction of solutions to all of the the quantum constraints in the Ashtekar variables and their associated Hilbert space. A physical Hilbert space is constructed for Lorentzian signature gravity with nonzero cosmological constant in the form of unitary, irreducible representations of the affine group.
Irreducible quantum group modules with finite dimensional weight spaces
DEFF Research Database (Denmark)
Pedersen, Dennis Hasselstrøm
We classify all irreducible weight modules for a quantized enveloping algebra U q (g) at most q ∈ C ∗ when the simple Lie algebra g is not of type G 2 . More precisely, our classificiation is carried out when q is either an odd root of unity or transcendental over Q. By a weight module we mean a ...... not present in the classical case. In the process we also construct twisting functors rigerously for quantum group modules, study twisted Verma modules and show that these admit a Jantzen filtration with corresponding Jantzen sum formula....
Extended-Lorentz Quantum-Cosmology Symmetry Group
Chew, Geoffrey F
2013-01-01
Unitarily representable by transformations of Milne quantum-universe (MQU) Hilbert-space vectors is a 9-parameter 'extended-Lorentz' Lie group whose algebra comprises 9 conserved MQU-constituent ('quc') attributes: electric charge, energy, spirality, 3-vector momentum and 3-vector angular momentum. Commutation with the full symmetry algebra by the 3-element Lorentz-extending sub-algebra identifies any quc by its (permanent) trio of charge, spirality and energy integers. Milne's redshift-specifying 'universe age' is invariant under the MQU symmetry group. Also invariant is the (elsewhere specified) universe hamiltonian--a self-adjoint age-dependent Hilbert-space operator (not a symmetry-algebra member) that generates universe evolution with increasing age through a 'Schrodinger' (first-order) differential equation.
Group Theoretical Approach for Controlled Quantum Mechanical Systems
National Research Council Canada - National Science Library
Tarn, Tzyh-Jong
2007-01-01
The aim of this research is the study of controllability of quantum mechanical systems and feedback control of de-coherence in order to gain an insight on the structure of control of quantum systems...
Static solutions of SU(2)-Higgs theory
Energy Technology Data Exchange (ETDEWEB)
Yaffe, L.G. (Department of Physics, FM-15, University of Washington, Seattle, Washington 98195 (US))
1989-11-15
The structure and stability of static spherically symmetric solutions in the SU(2)-Higgs theory are examined using both analytic and numerical methods. Accurate results are presented for the energy and instability growth rates of the sphaleron'' solution as a function of the Higgs-boson mass. The sphaleron is shown to undergo an infinite sequence of bifurcations as the Higgs-boson mass is increased, starting at {ital M}{sub {ital H}}=12M{sub W}. New deformed sphaleron'' solutions emerge from each of these bifurcations. These deformed sphalerons are not charge-conjugation invariant, have non-half-integral winding numbers, and are lower in energy than the original sphaleron. Hence, for sufficiently large Higgs-boson mass, minimal-energy paths connecting inequivalent vacuum states do not pass through the original sphaleron configuration.
Entangled SU(2) and SU(1,1) coherent states
Wang, Xiao-Guang; Sanders, Barry C.; Pan, Shao-Hua
2000-01-01
Entangled SU(2) and SU(1,1) coherent states are developed as superpositions of multiparticle SU(2) and SU(1,1) coherent states. In certain cases, these are coherent states with respect to generalized su(2) and su(1,1) generators, and multiparticle parity states arise as a special case. As a special example of entangled SU(2) coherent states, entangled binomial states are introduced and these entangled binomial states enable the contraction from entangled SU(2) coherent states to entangled har...
Minimal affinizations of representations of quantum groups: the irregular case
Chari, Vyjayanthi; Pressley, Andrew
1996-03-01
Letmathfrak{g} be a finite-dimensional complex simple Lie algebra and Uq(mathfrak{g}) the associated quantum group ( q is a nonzero complex number which we assume is transcendental). If V is a finitedimensional irreducible representation of Uq(mathfrak{g}), an affinization of V is an irreducible representation VV of the quantum affine algebra Uq(hat {mathfrak{g}}) which contains V with multiplicity one and is such that all other irreducible Uq(mathfrak{g})-components of V have highest weight strictly smaller than the highest weight λ of V. There is a natural partial order on the set of Uq(mathfrak{g}) classes of affinizations, and we look for the minimal one(s). In earlier papers, we showed that (i) ifmathfrak{g} is of type A, B, C, F or G, the minimal affinization is unique up to Uq(mathfrak{g})-isomorphism; (ii) ifmathfrak{g} is of type D or E and λ is not orthogonal to the triple node of the Dynkin diagram ofmathfrak{g}, there are either one or three minimal affinizations (depending on λ). In this paper, we show, in contrast to the regular case, that if Uq(mathfrak{g}) is of type D 4 and λ is orthogonal to the triple node, the number of minimal affinizations has no upper bound independent of λ. As a by-product of our methods, we disprove a conjecture according to which, ifmathfrak{g} is of type A n,every affinization is isomorphic to a tensor product of representations of Uq(hat {mathfrak{g}}) which are irreducible under Uq(mathfrak{g}) (in an earlier paper, we proved this conjecture when n=1).
L^2-Betti numbers of rigid C*-tensor categories and discrete quantum groups
DEFF Research Database (Denmark)
Kyed, David; Raum, Sven; Vaes, Stefaan
2017-01-01
of the representation category $Rep(G)$ and thus, in particular, invariant under monoidal equivalence. As an application, we obtain several new computations of $L^2$-Betti numbers for discrete quantum groups, including the quantum permutation groups and the free wreath product groups. Finally, we obtain upper bounds...
A quantum proxy group signature scheme based on an entangled five-qubit state
Wang, Meiling; Ma, Wenping; Wang, Lili; Yin, Xunru
2015-09-01
A quantum proxy group signature (QPGS) scheme based on controlled teleportation is presented, by using the entangled five-qubit quantum state functions as quantum channel. The scheme uses the physical characteristics of quantum mechanics to implement delegation, signature and verification. The security of the scheme is guaranteed by the entanglement correlations of the entangled five-qubit state, the secret keys based on the quantum key distribution (QKD) and the one-time pad algorithm, all of which have been proven to be unconditionally secure and the signature anonymity.
Phase space picture of quantum mechanics group theoretical approach
Kim, Y S
1991-01-01
This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.
2011-09-12
... COMMISSION Dialpoint Communications Corp., Pacel Corp., Quantum Group, Inc. (The), and Tradequest... Communications Corp. because it has not filed any periodic reports since the period ended September 30, 2008. It... accurate information concerning the securities of Quantum Group, Inc. (The) because it has not filed any...
A new class of group field theories for 1st order discrete quantum gravity
Oriti, D.; Tlas, T.
2008-01-01
Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any choice of spacetime dimension and signature, whose Feynman
Wu, Xiang-Yao; Liu, Xiao-Jing; Li, Hong; Zhang, Si-Qi; Ma, Ji; Liu, Ji-Ping; Liang, Yu
2017-10-01
In this paper, we have proposed S U(2) non-Abelian electromagnetism gauge theory. In the theory, photon has self-interaction and interaction between them, which can explain photon entanglement phenomenon in quantum information. Otherwise, we find there are three kinds photons γ +, γ - and γ 0, they have electric charge + e γ , - e γ and 0, respectively, these prediction are accordance with some experiment results.
Energy Technology Data Exchange (ETDEWEB)
Campigotto, C.
1993-12-01
The first part is concerned with the introduction of quantum groups as an extension of Lie groups. In particular, we study the case of unitary enveloping algebras in dimension 2. We then connect the quantum group formalism to the construction of g CGC recurrent relations. In addition, we construct g-deformed Krawtchouck and Meixner orthogonal polynomials and list their respective main characteristics. The second part deals with some dynamical systems from a classical, a quantum and a gp-analogue point of view. We investigate the Coulomb Kepler system by using the canonical namical systems which contain as special cases some interesting systems for nuclear of atomic physics and for quantum chemistry, such as the Hartmann system, the ring-shaped oscillator, the Smarodinsky-Winternitz system, the Aharonov-Bohen system and the dyania of Dirac and Schroedinger. (author). 291 refs.
Summary of working group activities in non-perturbative quantum ...
Indian Academy of Sciences (India)
quantum chromodynamics (lattice gauge theory). PUSHAN MAJUMDAR. Department of Theoretical Physics, Indian Association for the Cultivation of Science, ... Wilson–Dirac operator which is denoted as DW. However, this Dirac operator breaks chiral symmetry explicitly. Till date the best that can be done is to write down a ...
Lin, Yu-Ping; Kao, Ying-Jer; Chen, Pochung; Lin, Yu-Cheng
2017-08-01
The antiferromagnetic Ising chain in both transverse and longitudinal magnetic fields is one of the paradigmatic models of a quantum phase transition. The antiferromagnetic system exhibits a zero-temperature critical line separating an antiferromagnetic phase and a paramagnetic phase; the critical line connects an integrable quantum critical point at zero longitudinal field and a classical first-order transition point at zero transverse field. Using a strong-disorder renormalization group method formulated as a tree tensor network, we study the zero-temperature phase of the quantum Ising chain with bond randomness. We introduce a new matrix product operator representation of high-order moments, which provides an efficient and accurate tool for determining quantum phase transitions via the Binder cumulant of the order parameter. Our results demonstrate an infinite-randomness quantum critical point in zero longitudinal field accompanied by pronounced quantum Griffiths singularities, arising from rare ordered regions with anomalously slow fluctuations inside the paramagnetic phase. The strong Griffiths effects are signaled by a large dynamical exponent z >1 , which characterizes a power-law density of low-energy states of the localized rare regions and becomes infinite at the quantum critical point. Upon application of a longitudinal field, the quantum phase transition between the paramagnetic phase and the antiferromagnetic phase is completely destroyed. Furthermore, quantum Griffiths effects are suppressed, showing z <1 , when the dynamics of the rare regions is hampered by the longitudinal field.
A Third-Party E-Payment Protocol Based on Quantum Group Blind Signature
Zhang, Jian-Zhong; Yang, Yuan-Yuan; Xie, Shu-Cui
2017-09-01
A third-party E-payment protocol based on quantum group blind signature is proposed in this paper. Our E-payment protocol could protect user's anonymity as the traditional E-payment systems do, and also have unconditional security which the classical E-payment systems can not provide. To achieve that, quantum key distribution, one-time pad and quantum group blind signature are adopted in our scheme. Furthermore, if there were a dispute, the manager Trent can identify who tells a lie.
Involutive representations of coordinate algebras and quantum spaces
Jurić, Tajron; Poulain, Timothé; Wallet, Jean-Christophe
2017-07-01
We show that su(2) Lie algebras of coordinate operators related to quantum spaces with su(2) noncommutativity can be conveniently represented by SO(3)-covariant poly-differential involutive representations. We show that the quantized plane waves ob-tained from the quantization map action on the usual exponential functions are determined by polar decomposition of operators combined with constraint stemming from the Wigner theorem for SU(2). Selecting a subfamily of ∗-representations, we show that the resulting star-product is equivalent to the Kontsevich product for the Poisson manifold dual to the finite dimensional Lie algebra su(2) . We discuss the results, indicating a way to extend the construction to any semi-simple non simply connected Lie group and present noncommutative scalar field theories which are free from perturbative UV/IR mixing.
Construction of the Bethe State for the $E_{tau,eta(so_3$ Elliptic Quantum Group
Directory of Open Access Journals (Sweden)
Nenad Manojlović
2007-01-01
Full Text Available Elliptic quantum groups can be associated to solutions of the star-triangle relation of statistical mechanics. In this paper, we consider the particular case of the $E_{tau,eta(so_3$ elliptic quantum group. In the context of algebraic Bethe ansatz, we construct the corresponding Bethe creation operator for the transfer matrix defined in an arbitrary representation of $E_{tau,eta(so_3$.
Confining vs. conformal scenario for SU(2) with 2 adjoint fermions. Mesonic spectrum
DEFF Research Database (Denmark)
Pica, Claudio; Del Debbio, Luigi; Lucini, Biagio
2010-01-01
The Minimal Walking Technicolor (MWT) model, based on the SU(2) gauge group with two Dirac adjoint fermions, is expected to lie close to the lower boundary of the conformal window. As such, it is believed to possess a dynamics different enough from QCD to be a viable candidate for a Technicolor t...
Weinberg Angle Derivation from Discrete Subgroups of SU(2 and All That
Directory of Open Access Journals (Sweden)
Potter F.
2015-01-01
Full Text Available The Weinberg angle W of the Standard Model of leptons and quarks is derived from specific discrete (i.e., finite subgroups of the electroweak local gauge group SU(2 L U(1 Y . In addition, the cancellation of the triangle anomaly is achieved even when there are four quark families and three lepton families!
Running coupling in SU(2) gauge theory with two adjoint fermions
DEFF Research Database (Denmark)
Rantaharju, Jarno; Rantalaiho, Teemu; Rummukainen, Kari
2016-01-01
We study SU(2) gauge theory with two Dirac fermions in the adjoint representation of the gauge group on the lattice. Using clover improved Wilson fermion action with hypercubic truncated stout smearing we perform simulations at larger coupling than before. We measure the evolution of the coupling...
Noether’s theorem for dissipative quantum dynamical semi-groups
Energy Technology Data Exchange (ETDEWEB)
Gough, John E., E-mail: jug@aber.ac.uk [Aberystwyth University, Aberystwyth SY23 3BZ, Wales (United Kingdom); Ratiu, Tudor S., E-mail: tudor.ratiu@epfl.ch [Section de Mathématiques and Bernoulli Center, École Polytechnique Fédérale de Lausanne, Lausanne CH 1015 (Switzerland); Smolyanov, Oleg G., E-mail: smolyanov@yandex.ru [Mechanics and Mathematics Faculty, Moscow State University, Moscow 119991 (Russian Federation)
2015-02-15
Noether’s theorem on constants of the motion of dynamical systems has recently been extended to classical dissipative systems (Markovian semi-groups) by Baez and Fong [J. Math. Phys. 54, 013301 (2013)]. We show how to extend these results to the fully quantum setting of quantum Markov dynamics. For finite-dimensional Hilbert spaces, we construct a mapping from observables to completely positive maps that leads to the natural analogue of their criterion of commutativity with the infinitesimal generator of the Markov dynamics. Using standard results on the relaxation of states to equilibrium under quantum dynamical semi-groups, we are able to characterise the constants of the motion under quantum Markov evolutions in the infinite-dimensional setting under the usual assumption of existence of a stationary strictly positive density matrix. In particular, the Noether constants are identified with the fixed point of the Heisenberg picture semi-group.
Energy Technology Data Exchange (ETDEWEB)
MacGregor, B.R.; McCoy, A.E.; Wickramasekara, S., E-mail: wickrama@grinnell.edu
2012-09-15
We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these representations determine the structure of quantum mechanics in non-inertial reference frames. Our representations of the Galilean line group contain the usual unitary projective representations of the Galilei group, but have a more intricate cocycle structure. The transformation formula for the Hamiltonian under the Galilean line group shows that in a non-inertial reference frame it acquires a fictitious potential energy term that is proportional to the inertial mass, suggesting the equivalence of inertial mass and gravitational mass in quantum mechanics. - Highlights: Black-Right-Pointing-Pointer A formulation of Galilean quantum mechanics in non-inertial reference frames is given. Black-Right-Pointing-Pointer The key concept is the Galilean line group, an infinite dimensional group. Black-Right-Pointing-Pointer Unitary, cocycle representations of the Galilean line group are constructed. Black-Right-Pointing-Pointer A non-central extension of the group underlies these representations. Black-Right-Pointing-Pointer Quantum equivalence principle and gravity emerge from these representations.
Effective SU(2) theory for the pseudogap state
Montiel, X.; Kloss, T.; Pépin, C.
2017-03-01
This paper exposes in a detailed manner the recent findings about the SU(2) scenario for the underdoped phase of the cuprate superconductors. The SU(2) symmetry is formulated as a rotation between the d -wave superconducting (SC) phase and a d -wave charge order. We define the operators responsible for the SU(2) rotations and we derive the nonlinear σ model associated with it. In this framework, we demonstrate that SU(2) fluctuations are massless in finite portions of the Brillouin zone corresponding to the antinodal regions (0 ,π ) and (π ,0 ). We argue that the presence of SU(2) fluctuations in the antinodal region leads to the opening of Fermi arcs around the Fermi surface and to the formation of the pseudogap. Moreover, we show that SU(2) fluctuations lead, in turn, to the emergence of a finite momentum SC order—or pair density wave (PDW)—and more importantly to a new kind of excitonic particle-hole pairs liquid, the resonant excitonic state (RES), which is made of patches of preformed particle-hole pairs with multiple momenta. When the RES liquid becomes critical, we demonstrate that electronic scattering through the critical modes leads to anomalous transport properties. This new finding can account for the strange metal (SM) phase at finite temperature, on the right-hand side of the SC dome, shedding light on another notoriously mysterious part of the phase diagram of the cuprates.
Classical and Quantum Burgers Fluids: A Challenge for Group Analysis
Directory of Open Access Journals (Sweden)
Philip Broadbridge
2015-10-01
Full Text Available The most general second order irrotational vector field evolution equation is constructed, that can be transformed to a single equation for the Cole–Hopf potential. The exact solution to the radial Burgers equation, with constant mass influx through a spherical supply surface, is constructed. The complex linear Schrödinger equation is equivalent to an integrable system of two coupled real vector equations of Burgers type. The first velocity field is the particle current divided by particle probability density. The second vector field gives a complex valued correction to the velocity that results in the correct quantum mechanical correction to the kinetic energy density of the Madelung fluid. It is proposed how to use symmetry analysis to systematically search for other constrained potential systems that generate a closed system of vector component evolution equations with constraints other than irrotationality.
Supersymmetry Breaking Threshold Corrections in the $SU(4)\\times SU(2)_L\\times SU(2)_R$ Model
Korakianitis, O.; Tracas, N. D.
1993-01-01
We evaluate the SUSY and top threshold effects in the context of the MSSM and the string derived model based on SU(4)$\\times$SU(2)$_L\\times$SU(2)$_R$. In both cases we run the two loop RGEs and determine the lower bounds of the supersymmetric particle masses, dictated by the experimentally accepted regions of the values of the low energy parameters.
Thermodynamics of SU(2) mathcal{N} =2 supersymmetric Yang-Mills theory
Paik, Steve; Yaffe, Laurence G.
2010-01-01
The thermodynamics of four-dimensional SU(2) mathcal{N} =2 super-Yang-Mills theory is examined in both high and low temperature regimes. At low temperatures, compelling evidence is found for two distinct equilibrium states related by a spontaneously broken discrete R-symmetry. These equilibrium states exist because the quantum moduli space of the theory has two singular points where extra massless states appear. At high temperature, a unique R-symmetry-preserving equilibrium state is found. Discrepancies with previous results in the literature are explained.
Energy Technology Data Exchange (ETDEWEB)
Pruschke, Th., E-mail: pruschke@theorie.physik.uni-goettingen.d [Insitute for Theoretical Physics, University of Goettingen, Friedrich-Hund-Platz 1, 37077 Goetingen (Germany); Dirks, A.; Gezzi, R. [Insitute for Theoretical Physics, University of Goettingen, Friedrich-Hund-Platz 1, 37077 Goetingen (Germany)
2009-10-15
We present an extension of the concepts of the functional renormalization group approach to quantum many-body problems in non-equilibrium situations. The approach is completely general and allows calculations for both stationary and time-dependent situations. As a specific example we study the stationary state transport through a quantum dot with local Coulomb correlations. We discuss the influence of finite bias voltage and temperature on the current and conductance.
Light Kaluza Klein States in Randall-Sundrum Models with Custodial SU(2)
Energy Technology Data Exchange (ETDEWEB)
Carena, Marcela; /Fermilab; Ponton, Eduardo; /Columbia U.; Santiago, Jose; /Fermilab; Wagner, Carlos E.M.; /Argonne /Chicago U., EFI /KICP, Chicago
2006-07-01
We consider Randall-Sundrum scenarios based on SU(2){sub L} x SU(2){sub R} and a discrete parity exchanging L with R. The custodial and parity symmetries can be used to make the tree level contribution to the T parameter and the anomalous couplings of the bottom quark to the Z very small. We show that the resulting quantum numbers typically induce a negative T parameter at one loop that, together with the positive value of the S parameter, restrict considerably these models. There are nevertheless regions of parameter space that successfully reproduce the fit to electroweak precision observables with light Kaluza-Klein excitations accessible at colliders. We consider models of gauge-Higgs unification that implement the custodial and parity symmetries and find that the electroweak data singles out a very well defined region in parameter space. In this region one typically finds light gauge boson Kaluza-Klein excitations as well as light SU(2){sub L} singlet, and sometimes also doublet, fermionic states, that mix with the top quark, and that may yield interesting signatures at future colliders.
Quasi-quantum groups, knots, three-manifolds, and topological field theory
Altschüler, D R; Altschuler, Daniel; Coste, Antoine
1992-01-01
We show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This happens for a finite-dimensional quasi-quantum group, whose definition involves a finite group $G$, and a 3-cocycle $\\om$, which was first studied by Dijkgraaf, Pasquier and Roche. We treat this example in more detail, and argue that in this case the invariants agree with the partition function of the topological field theory of Dijkgraaf and Witten depending on the same data $G, \\,\\om$.
Endomorphism Algebras of Tensor Powers of Modules for Quantum Groups
DEFF Research Database (Denmark)
Andersen, Therese Søby
the group algebra of the braid group to the endomorphism algebra of any tensor power of the Weyl module with highest weight 2. We take a first step towards determining the kernel of this map by reformulating well-known results on the semisimplicity of the Birman-Murakami-Wenzl algebra in terms of the order...
Liu, X M; Cheng, W W; Liu, J-M
2016-01-19
We investigate the quantum Fisher information and quantum phase transitions of an XY spin chain with staggered Dzyaloshinskii-Moriya interaction using the quantum renormalization-group method. The quantum Fisher information, its first-derivatives, and the finite-size scaling behaviors are rigorously calculated respectively. The singularity of the derivatives at the phase transition point as a function of lattice size is carefully discussed and it is revealed that the scaling exponent for quantum Fisher information at the critical point can be used to describe the correlation length of this model, addressing the substantial role of staggered Dzyaloshinskii-Moriya interaction in modulating quantum phase transitions.
Energy Technology Data Exchange (ETDEWEB)
Corrigan, E., E-mail: edward.corrigan@durham.ac.u [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom); Zambon, C., E-mail: cristina.zambon@durham.ac.u [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom)
2011-07-21
Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang-Baxter equations, and second by solving a linear intertwining relation between a finite-dimensional representation of the relevant Borel subalgebra of the quantum group underpinning the integrable quantum field theory and a particular infinite-dimensional representation expressed in terms of sets of generalised 'quantum' annihilation and creation operators. The principal examples analysed are based on the a{sub 2}{sup (2)} and a{sub n}{sup (1)} affine Toda models but examples of similar infinite-dimensional representations for quantum Borel algebras for all other affine Toda theories are also provided.
Finite number of states, de Sitter space and quantum groups at roots of unity
Energy Technology Data Exchange (ETDEWEB)
Pouliot, Philippe [Physics Department, Queen Mary, University of London, London E1 4NS (United Kingdom)
2004-01-07
This paper explores the use of a deformation by a root of unity as a tool to build models with a finite number of states for applications to quantum gravity. The initial motivation for this work was cosmological breaking of supersymmetry. We explain why the project was unsuccessful. What is left are some observations on supersymmetry for q-bosons, an analogy between black holes in de Sitter and properties of quantum groups, and an observation on a noncommutative quantum mechanics model with two degrees of freedom, depending on one parameter. When this parameter is positive, the spectrum has a finite number of states; when it is negative or zero, the spectrum has an infinite number of states. This exhibits a desirable feature of quantum physics in de Sitter space, albeit in a very simple, non-gravitational context.
Klevers, Denis
2016-01-01
We give an explicit construction of a class of F-theory models with matter in the three-index symmetric (4) representation of SU(2). This matter is realized at codimension two loci in the F-theory base where the divisor carrying the gauge group is singular; the associated Weierstrass model does not have the form associated with a generic SU(2) Tate model. For 6D theories, the matter is localized at a triple point singularity of arithmetic genus g=3 in the curve supporting the SU(2) group. This is the first explicit realization of matter in F-theory in a representation corresponding to a genus contribution greater than one. The construction is realized by "unHiggsing" a model with a U(1) gauge factor under which there is matter with charge q=3. The resulting SU(2) models can be further unHiggsed to realize non-Abelian G_2xSU(2) models with more conventional matter content or SU(2)^3 models with trifundamental matter. The U(1) models used as the basis for this construction do not seem to have a Weierstrass real...
Phase diagram of the lattice SU(2) Higgs model
Energy Technology Data Exchange (ETDEWEB)
Bonati, C., E-mail: bonati@df.unipi.i [Dipartimento di Fisica and INFN, Pisa (Italy); Cossu, G., E-mail: cossu@post.kek.j [Scuola Normale Superiore and INFN, Pisa (Italy); D' Elia, M., E-mail: Massimo.Delia@ge.infn.i [Dipartimento di Fisica and INFN, Genova (Italy); Di Giacomo, A., E-mail: digiaco@df.unipi.i [Dipartimento di Fisica and INFN, Pisa (Italy)
2010-03-21
We perform a detailed study of the phase diagram of the lattice Higgs SU(2) model with fixed Higgs field length. Consistently with previsions based on the Fradkin-Shenker theorem we find a first order transition line with an endpoint whose position we determined. The diagram also shows cross-over lines: the cross-over corresponding to the pure SU(2) bulk is also present at nonzero coupling with the Higgs field and merges with the one that continues the line of first order transition beyond the critical endpoint. At high temperature the first order line becomes a crossover, whose position moves by varying the temperature.
Polyakov loop percolation and deconfinement in SU(2) gauge theory
Fortunato, S.; Satz, H.
2000-03-01
The deconfinement transition in /SU(2) gauge theory and the magnetization transition in the Ising model belong to the same universality class. The critical behaviour of the Ising model can be characterized either as spontaneous breaking of the Z2 symmetry of spin states or as percolation of appropriately defined spin clusters. We show that deconfinement in /SU(2) gauge theory can be specified as percolation of Polyakov loop clusters with Fortuin-Kasteleyn bond weights, leading to the same (Onsager) critical exponents as the conventional order-disorder description based on the Polykov loop expectation value.
Effective geometric phases and topological transitions in SO(3) and SU(2) rotations.
Saarikoski, Henri; Baltanás, José Pablo; Vázquez-Lozano, J Enrique; Nitta, Junsaku; Frustaglia, Diego
2016-04-27
We address the development of geometric phases in classical and quantum magnetic moments (spin-1/2) precessing in an external magnetic field. We show that nonadiabatic dynamics lead to a topological phase transition determined by a change in the driving field topology. The transition is associated with an effective geometric phase which is identified from the paths of the magnetic moments in a spherical geometry. The topological transition presents close similarities between SO(3) and SU(2) cases but features differences in, e.g. the adiabatic limits of the geometric phases, being 2π and π in the classical and the quantum case, respectively. We discuss possible experiments where the effective geometric phase would be observable.
Quantum mechanics and spectrum generating groups and supergroups
Energy Technology Data Exchange (ETDEWEB)
Bohm, A.
1986-04-01
Collective models are reviewed briefly as the physical basis for dynamical groups, particularly for molecular and nuclear physics. To show that collective models for extended relativistic objects can be constructed, the results of a quantal relativistic oscillator are reviewed. An infinite supermultiplet is then used to describe Regge recurrences as yrast states and daughters as radial excitations. (LEW)
Four-dimensional quantum oscillator and magnetic monopole with U(1) dynamical group
Bakhshi, Z.; Panahi, H.; Golchehre, S. G.
2017-09-01
By using an appropriate transformation, it was shown that the quantum system of four-dimensional (4D) simple harmonic oscillator can describe the motion of a charged particle in the presence of a magnetic monopole field. It was shown that the Dirac magnetic monopole has the hidden algebra of U(1) symmetry and by reducing the dimensions of space, the U(1) × U(1) dynamical group for 4D harmonic oscillator quantum system was obtained. Using the group representation and based on explicit solution of the obtained differential equation, the spectrum of system was calculated.
Group field theory for quantum gravity minimally coupled to a scalar field
Li, Yang; Oriti, Daniele; Zhang, Mingyi
2017-10-01
We construct a group field theory model for quantum gravity minimally coupled to relativistic scalar fields, defining as well a corresponding discrete gravity path integral (and, implicitly, a coupled spin foam model) in its Feynman expansion. We also analyze a number of variations of the same model, the corresponding discrete gravity path integrals, its generalization to the coupling of multiple scalar fields and discuss its possible applications to the extraction of effective cosmological dynamics from the full quantum gravity formalism, in the context of group field theory condensate cosmology.
't Hooft loop and the phases of SU(2) LGT
Burgio, Giuseppe
2013-01-01
We analyze the vacuum structure of SU(2) lattice gauge theories in D=2,3,4, concentrating on the stability of 't Hooft loops. High precision calculations have been performed in D=3; similar results hold also for D=4 and D=2. We discuss the impact of our findings on the continuum limit of Yang-Mills theories.
Mass anomalous dimension in SU(2) with six fundamental fermions
DEFF Research Database (Denmark)
Bursa, Francis; Del Debbio, Luigi; Keegan, Liam
2010-01-01
We simulate SU(2) gauge theory with six massless fundamental Dirac fermions. We measure the running of the coupling and the mass in the Schroedinger Functional scheme. We observe very slow running of the coupling constant. We measure the mass anomalous dimension gamma, and find it is between 0.13...
The SU(2)-Higgs model on asymmetric lattices
Csikor, Ferenc
1996-01-01
We calculate the {\\cal O}(g^2,\\lambda) corrections to the coupling anisotropies of the SU(2)-Higgs model on lattices with asymmetric lattice spacings. These corrections are obtained by a one-loop calculation requiring the rotational invariance of the gauge- and Higgs-boson propagators in the continuum limit.
Large-volume results in SU(2) with adjoint fermions
Del Debbio, Luigi; Pica, Claudio; Patella, Agostino; Rago, Antonio; Roman, Sabin
2014-01-01
Taming finite-volume effects is a crucial ingredient in order to identify the existence of IR fixed points. We present the latest results from our numerical simulations of SU(2) gauge theory with 2 Dirac fermions in the adjoint representation on large volumes. We compare with previous results, and extrapolate to thermodynamic limit when possible.
Finite volume effects in SU(2) with two adjoint fermions
DEFF Research Database (Denmark)
Del Debbio, Luigi; Lucini, Biagio; Patella, Agostino
2011-01-01
Many evidences from lattice simulations support the idea that SU(2) with two Dirac flavors in the adjoint representation (also called Minimal Walking Technicolor) is IR conformal. A possible way to see this is through the behavior of the spectrum of the mass-deformed theory. When fermions are mas...
Large-volume results in SU(2) with adjoint fermions
DEFF Research Database (Denmark)
Del Debbio, Luigi; Lucini, Biagio; Pica, Claudio
2013-01-01
Taming finite-volume effects is a crucial ingredient in order to identify the existence of IR fixed points. We present the latest results from our numerical simulations of SU(2) gauge theory with 2 Dirac fermions in the adjoint representation on large volumes. We compare with previous results, an...
Compactifications of IIA supergravity on SU(2)-structure manifolds
Energy Technology Data Exchange (ETDEWEB)
Spanjaard, B.
2008-07-15
In this thesis, we study compactifications of type IIA supergravity on six-dimensional manifolds with an SU(2)-structure. A general study of six-dimensional manifolds with SU(2)-structure shows that IIA supergravity compactified on such a manifold should yield a four-dimensional gauged N=4 supergravity. We explicitly derive the bosonic spectrum, gauge transformations and action for IIA supergravity compactified on two different manifolds with SU(2)-structure, one of which also has an H{sup (3)}{sub 10}-flux, and confirm that the resulting four-dimensional theories are indeed N=4 gauged supergravities. In the second chapter, we study an explicit construction of a set of SU(2)-structure manifolds. This construction involves a Scherk-Schwarz duality twist reduction of the half-maximal six-dimensional supergravity obtained by compactifying IIA supergravity on a K3. This reduction results in a gauged N=4 four-dimensional supergravity, where the gaugings can be divided into three classes of parameters. We relate two of the classes to parameters we found before, and argue that the third class of parameters could be interpreted as a mirror flux. (orig.)
Directory of Open Access Journals (Sweden)
Alexis De Vos
2011-06-01
Full Text Available Whereas quantum computing circuits follow the symmetries of the unitary Lie group, classical reversible computation circuits follow the symmetries of a finite group, i.e., the symmetric group. We confront the decomposition of an arbitrary classical reversible circuit with w bits and the decomposition of an arbitrary quantum circuit with w qubits. Both decompositions use the control gate as building block, i.e., a circuit transforming only one (qubit, the transformation being controlled by the other w−1 (qubits. We explain why the former circuit can be decomposed into 2w − 1 control gates, whereas the latter circuit needs 2w − 1 control gates. We investigate whether computer circuits, not based on the full unitary group but instead on a subgroup of the unitary group, may be decomposable either into 2w − 1 or into 2w − 1 control gates.
Quantum Critical Spin-2 Chain with Emergent SU(3) Symmetry
Chen, Pochung; Xue, Zhi-Long; McCulloch, I. P.; Chung, Ming-Chiang; Huang, Chao-Chun; Yip, S.-K.
2015-04-01
We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU (3 )1 Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.
Quantum critical spin-2 chain with emergent SU(3) symmetry.
Chen, Pochung; Xue, Zhi-Long; McCulloch, I P; Chung, Ming-Chiang; Huang, Chao-Chun; Yip, S-K
2015-04-10
We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)_{1} Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.
Measurement of the velocity of a quantum object: A role of phase and group velocities
Lapinski, Mikaila; Rostovtsev, Yuri V.
2017-08-01
We consider the motion of a quantum particle in a free space. Introducing an explicit measurement procedure for velocity, we demonstrate that the measured velocity is related to the group and phase velocities of the corresponding matter waves. We show that for long distances the measured velocity coincides with the matter wave group velocity. We discuss the possibilities to demonstrate these effects for the optical pulses in coherently driven media or for radiation propagating in waveguides.
Energy Technology Data Exchange (ETDEWEB)
Pilla, Viviane, E-mail: vivianepilla@infis.ufu.br [Universidade Federal de Uberlandia (UFU), Instituto de Fisica (Brazil); Munin, Egberto [Universidade Camilo Castelo Branco (UNICASTELO), Centro de Engenharia Biomedica (Brazil)
2012-10-15
The thermo-optical parameters of cadmium selenide/zinc sulfide (CdSe/ZnS) core-shell quantum dots (QDs) suspended in aqueous solutions were measured using a Thermal Lens (TL) technique. TL transient measurements were performed using the mode-mismatched dual-beam (excitation and probe) configuration. A He-Ne laser at {lambda}{sub p} = 632.8 nm was used as the probe beam, and an Ar{sup +} laser (at {lambda}{sub e} = 514.5 nm) was used as the excitation beam to study the effect of the core sizes (2-4 nm) of CdSe/ZnS nanocrystals functionalized with amine (R-NH{sub 2}) or carboxyl (R-COOH) groups. The average values of the thermal diffusivity D = (1.48 {+-} 0.06) Multiplication-Sign 10{sup -3} cm{sup 2}/s obtained for QDs samples are in good agreement with the pure water solvent result. The fraction thermal load ({phi}) and radiative quantum efficiencies ({eta}) of the functionalized CdSe/ZnS QDs were determined and compared with non-functionalized CdSe/ZnS QDs. The obtained {eta} values for non-functionalized CdSe/ZnS are slightly higher than those for the QDs functionalized with amine or carboxyl groups.
Mambrini, Matthieu; Poilblanc, Didier
2016-01-01
We elaborate a simple classification scheme of all rank-5 SU(2)-spin rotational symmetric tensors according to i) the on-site physical spin-$S$, (ii) the local Hilbert space $V^{\\otimes 4}$ of the four virtual (composite) spins attached to each site and (iii) the irreducible representations of the $C_{4v}$ point group of the square lattice. We apply our scheme to draw a complete list of all SU(2)-symmetric translationally and rotationally-invariant Projected Entangled Pair States (PEPS) with bond dimension $D\\leqslant 6$. All known SU(2)-symmetric PEPS on the square lattice are recovered and simple generalizations are provided in some cases. More generally, to each of our symmetry class can be associated a $({\\cal D}-1)$-dimensional manifold of spin liquids (potentially) preserving lattice symmetries and defined in terms of ${\\cal D}$ independent tensors of a given bond dimension $D$. In addition, generic (low-dimensional) families of PEPS explicitly breaking either (i) particular point-group lattice symmetri...
Mass anomalous dimension in SU(2) with six fundamental fermions
Energy Technology Data Exchange (ETDEWEB)
Bursa, Francis, E-mail: fwb22@cam.ac.u [Jesus College, Cambridge, CB5 8BL (United Kingdom); Del Debbio, Luigi; Keegan, Liam [SUPA, School of Astrophysics and Astronomy, University of Edinburgh, Edinburgh, EH9 3JZ (United Kingdom); Pica, Claudio [CP3-Origins, University of Southern Denmark Odense, 5230 M (Denmark); Pickup, Thomas [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3NP (United Kingdom)
2011-02-07
We simulate SU(2) gauge theory with six massless fundamental Dirac fermions. We measure the running of the coupling and the mass in the Schroedinger Functional scheme. We observe very slow running of the coupling constant. We measure the mass anomalous dimension {gamma}, and find it is between 0.135 and 1.03 in the range of couplings consistent with the existence of an IR fixed point.
SU(2)-monopoles, curves with symmetries and Ramanujan's heritage
Braden, Harry W.; Ènol'skii, Viktor Z.
2010-08-01
We develop the Ercolani-Sinha construction of SU(2) monopoles for a five-parameter family of centred charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a number-theoretic problem and a recently proven identity of Ramanujan provides a solution. Bibliography: 36 titles.
Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-de Sitter Groups
Directory of Open Access Journals (Sweden)
Ángel Ballesteros
2017-01-01
Full Text Available The κ-deformation of the (2 + 1D anti-de Sitter, Poincaré, and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant is considered as an explicit parameter. The Drinfel’d-double and the Poisson–Lie structure underlying the κ-deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson–Lie algebras. As a consequence, the noncommutative (2 + 1D spacetimes that generalize the κ-Minkowski space to the (anti-de Sitter ones are obtained. Moreover, noncommutative 4D spaces of (time-like geodesics can be defined, and they can be interpreted as a novel possibility to introduce noncommutative worldlines. Furthermore, quantum (anti-de Sitter algebras are presented both in the known basis related to 2 + 1 quantum gravity and in a new one which generalizes the bicrossproduct one. In this framework, the quantum deformation parameter is related to the Planck length, and the existence of a kind of “duality” between the cosmological constant and the Planck scale is also envisaged.
Axion inflation with an SU(2) gauge field: detectable chiral gravity waves
Energy Technology Data Exchange (ETDEWEB)
Maleknejad, Azadeh [School of Physics, Institute for Research in Fundamental Sciences (IPM), P. Code. 19538-33511, Tehran (Iran, Islamic Republic of)
2016-07-20
We study a single field axion inflation model in the presence of an SU(2) gauge field with a small vev. In order to make the analysis as model-independent as possible, we consider an arbitrary potential for the axion that is able to support the slow-roll inflation. The gauge field is coupled to the axion with a Chern-Simons interaction (λ/f)F{sub μν}{sup a}F̃{sub a}{sup μν} where (λ/f)∼((O(10))/(M{sub pl})). It has a negligible effect on the background evolution, ((ρ{sub YM})/(M{sub pl}{sup 2}H{sup 2}))≲ϵ{sup 2}. However, its quantum fluctuations make a significant contribution to the cosmic perturbation. In particular, the gauge field has a spin-2 fluctuation which explicitly breaks the parity between the left- and right-handed polarization states. The chiral tensor modes are linearly coupled to the gravitational waves and lead to a circularly polarized tensor power spectrum comparable to the unpolarized vacuum power spectrum. Moreover, the scalar sector is modified by the linear scalar fluctuations of the gauge field. Since the spin-0 and spin-2 fluctuations of the SU(2) gauge field are independent, the gauge field can, at the same time, generate a detectable chiral gravitational wave signal and have a negligible contribution to the scalar fluctuations, in agreement with the current CMB observations.
Isomonodromic deformations and SU 2-invariant instantons on S4
Manasliski, Richard Muñiz
2009-07-01
Anti-self-dual (ASD) solutions to the Yang-Mills equation (or instantons) over an anti-self-dual 4-manifold, which are invariant under an appropriate action of a three-dimensional Lie group, give rise, via twistor construction, to isomonodromic deformations of connections on CP having four simple singularities. As is well known, such deformations are governed by the sixth Painlevé equation P VI(α,β,γ,δ). We work out the particular case of the SU-action on S4, obtained from the irreducible representation on R5. In particular, we express the parameters (α,β,γ,δ) in terms of the instanton number. The present paper contains the proof of the result announced in [Richard Muñiz Manasliski, Painlevé VI equation from invariant instantons, in: Geometric and Topological Methods for Quantum field theory, Contemp. Math., vol. 434, Amer. Math. Soc., Providence, RI, 2007, pp. 215-222].
Quantum groups as generalized gauge symmetries in WZNW models. Part I. The classical model
Hadjiivanov, L.; Furlan, P.
2017-07-01
Wess-Zumino-Novikov-Witten (WZNW) models over compact Lie groups G constitute the best studied class of (two dimensional, 2 D) rational conformal field theories (RCFTs). A WZNW chiral state space is a finite direct sum of integrable representations of the corresponding affine (current) algebra, and the correlation functions of primary fields are monodromy invariant combinations of left times right sector conformal blocks solving the Knizhnik-Zamolodchikov equation. However, even in this very well understood case of 2 D RCFT, the "internal" (gauge) symmetry that governs the ensuing fusion rules remains unclear. On the other hand, the canonical approach to the classical chiral WZNW theory developed by Faddeev, Alekseev, Shatashvili, Gawedzki and Falceto reveals its Poisson-Lie symmetry. After a covariant quantization, the latter gives rise to an associated quantum group symmetry which naturally requires an extension of the state space. This paper contains a review of earlier work on the subject with a special emphasis, in the case G = SU( n), on the emerging chiral "WZNW zero modes" which provide an adequate algebraic description of the internal symmetry structure of the model. Combining further left and right zero modes, one obtains a specific dynamical quantum group, the structure of its Fock representation resembling the axiomatic approach to gauge theories in which a "restricted" quantum group plays the role of a generalized gauge symmetry.
Density matrix renormalization group approach for many-body open quantum systems.
Rotureau, J; Michel, N; Nazarewicz, W; Płoszajczak, M; Dukelsky, J
2006-09-15
The density matrix renormalization group (DMRG) approach is extended to complex-symmetric density matrices characteristic of many-body open quantum systems. Within the continuum shell model, we investigate the interplay between many-body configuration interaction and coupling to open channels in case of the unbound nucleus (7)He. It is shown that the extended DMRG procedure provides a highly accurate treatment of the coupling to the nonresonant scattering continuum.
Arkhipov, S M; Odesskii, A V; Feigin, B; Vassiliev, V
1998-01-01
This volume presents the first collection of articles consisting entirely of work by faculty and students of the Higher Mathematics College of the Independent University of Moscow (IUM). This unique institution was established to train elite students to become research scientists. Covered in the book are two main topics: quantum groups and low-dimensional topology. The articles were written by participants of the Feigin and Vassiliev seminars, two of the most active seminars at the IUM.
Spin-Anisotropy Commensurable Chains: Quantum Group Symmetries and N=2 SUSY
Berkovich, A.; Gomez, C.; Sierra, G.
1993-01-01
In this paper we consider a class of the 2D integrable models. These models are higher spin XXZ chains with an extra condition of the commensurability between spin and anisotropy. The mathematics underlying this commensurability is provided by the quantum groups with deformation parameter being an Nth root of unity. Our discussion covers a range of topics including new integrable deformations, thermodynamics, conformal behaviour, S-matrices and magnetization. The emerging picture strongly dep...
The dual roles of functional groups in the photoluminescence of graphene quantum dots
Wang, Shujun; Cole, Ivan S.; Zhao, Dongyuan; Li, Qin
2016-03-01
The photoluminescent properties of graphene nanoparticle (named graphene quantum dots) have attracted significant research attention in recent years owing to their profound application potential. However, the photoluminescence (PL) origin of this class of nanocarbons is still unclear. In this paper, combining direct experimental evidence enabled by a facile size-tunable oxygenated graphene quantum dots (GQDs) synthesis method and theoretical calculations, the roles of the aromatic core, functional groups and disordered structures (i.e. defects and sp3 carbon) in the PL of oxygenated GQDs are elucidated in detail. In particular, we found that the functional groups on GQDs play dual roles in the overall emission: (1) they enable π* --> n and σ* --> n transitions, resulting in a molecular type of PL, spectrally invariable with change of particle size or excitation energy; (2) similar to defects and sp3 carbon, functional groups also induce structural deformation to the aromatic core, leading to mid-gap states or, in other words, energy traps, causing π* --> mid-gap states --> π transitions. Therefore, functional groups contribute to both the blue edge and the red shoulder of GQDs' PL spectra. The new insights on the role of functional groups in PL of fluorescent nanocarbons will enable better designs of this new class of materials.The photoluminescent properties of graphene nanoparticle (named graphene quantum dots) have attracted significant research attention in recent years owing to their profound application potential. However, the photoluminescence (PL) origin of this class of nanocarbons is still unclear. In this paper, combining direct experimental evidence enabled by a facile size-tunable oxygenated graphene quantum dots (GQDs) synthesis method and theoretical calculations, the roles of the aromatic core, functional groups and disordered structures (i.e. defects and sp3 carbon) in the PL of oxygenated GQDs are elucidated in detail. In particular, we found
Programs for generating Clebsch-Gordan coefficients of SU(3) in SU(2) and SO(3) bases
Bahri, C.; Rowe, D. J.; Draayer, J. P.
2004-05-01
Computer codes are developed to calculate Clebsch-Gordan coefficients of SU(3) in both SU(2)- and SO(3)-coupled bases. The efficiency of this code derives from the use of vector coherent state theory to evaluate the required coefficients directly without recursion relations. The approach extends to other compact semi-simple Lie groups. The codes are given in subroutine form so that users can incorporate the codes into other programs. Program summaryTitle of program: SU3CGVCS Catalogue identifier: ADTN Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTN Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: Persons requesting the program must sign the standard CPC non-profit use license Computers for which the program is designed and others on which it is operable: SGI Origin 2000, HP Apollo 9000, Sun, IBM SP, Pentium Operating systems under which the program has been tested: IRIX 6.5, HP UX 10.01, SunOS, AIX, Linux Programming language used: FORTRAN 77 Memory required to execute with typical data: On the HP system, it requires about 732 KBytes. Disk space used for output: 2100+2460 bytes No. of bits in a word: 32 bit integer and 64 bit floating point numbers. No. of processors used: 1 Has the code been vectorized: No No. of bytes in distributed program, including test data, etc.: 26 309 No. of lines in distributed program, including test data, etc.: 3969 Distribution format: tar gzip file Nature of physical problem: The group SU(3) and its Lie algebra su(3) have important applications, for example, in elementary particle physics, nuclear physics, and quantum optics [1-3]. The code presented is particularly relevant for the last two fields. Clebsch-Gordan (CG) coefficients are required whenever the symmetries of many-body systems are used for the evaluation of matrix elements of tensor operators. Moreover, the construction of CG coefficients for SU(3) serves as a nontrivial prototype for larger compact
Periodic Euclidean solutions of SU(2)-Higgs theory
Energy Technology Data Exchange (ETDEWEB)
Frost, K.L.; Yaffe, L.G. [University of Washington, Department of Physics, Seattle, Washington 98105-1560 (United States)
1999-03-01
We examine periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. Classical perturbation theory is used to construct periodic time-dependent solutions in the neighborhood of the static sphaleron. The behavior of the action, as a function of period, changes character depending on the value of the Higgs boson mass. The required pattern of bifurcations of solutions as a function of the Higgs boson mass is examined, and implications for the temperature dependence of the baryon number violation rate in the standard model are discussed. {copyright} {ital 1999} {ital The American Physical Society}
Tunneling Control of Transmission Coefficient and Group Index in a Quantum Dot Nanostructure
Directory of Open Access Journals (Sweden)
Hamid Reza Hamedi
2014-01-01
Full Text Available We theoretically study the transmission and group index properties of the probe field in a four-level quantum dot molecule. It is found that the tunnel coupling plays a very important role in realizing the transmission coefficient of the probe field. Moreover, the impact of an incoherent pump field on imaginary part of susceptibility is investigated. We show that probe transmission exhibits oppositional behavior against weak and strong incoherent pump rates. This approach allows substantial flexibility in the manipulation of group velocity of light.
Towards far-from-equilibrium quantum field dynamics: A functional renormalisation-group approach
Energy Technology Data Exchange (ETDEWEB)
Gasenzer, Thomas [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany)], E-mail: t.gasenzer@thphys.uni-heidelberg.de; Pawlowski, Jan M. [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany)
2008-12-11
Dynamic equations for quantum fields far from equilibrium are derived by use of functional renormalisation group techniques. The obtained equations are non-perturbative and lead substantially beyond mean-field and quantum Boltzmann type approximations. The approach is based on a regularised version of the generating functional for correlation functions where times greater than a chosen cutoff time are suppressed. As a central result, a time evolution equation for the non-equilibrium effective action is derived, and the time evolution of the Green functions is computed within a vertex expansion. It is shown that this agrees with the dynamics derived from the 1/N-expansion of the two-particle irreducible effective action.
Functional renormalisation group approach to far-from-equilibrium quantum field dynamics
Energy Technology Data Exchange (ETDEWEB)
Kessler, Stefan; Pawlowski, Jan M.; Gasenzer, Thomas [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany)
2008-07-01
We present a derivation of dynamic equations for quantum fields far from equilibrium by use of functional renormalisation group techniques. The obtained equations are non-perturbative and lead substantially beyond mean-field and quantum Boltzmann type approximations. The approach is based on a regularised version of the generating functional for correlation functions, where times greater than a chosen cutoff time are suppressed. As a central result a time evolution equation for the non-equilibrium effective action is derived. The time evolution of Green functions is computed within a vertex expansion. In a truncation of the flow equations the dynamic equations as known from the 1/N-expansion of the 2PI effective interaction are recovered.
Real-space renormalization-group studies of low-dimensional quantum antiferromagnets
Energy Technology Data Exchange (ETDEWEB)
Lepetit, M. (Laboratoire de Physique Quantique, Universite Paul Sabatier, 118 route de Narbonne, 31062 Toulouse CEDEX (France)); Manousakis, E. (Department of Physics, Center for Materials Research and Technology Supercomputer Computations Research Isntitute, Florida State University, Tallahassee, Florida 32306 (United States))
1993-07-01
We study the ground state of one- and two-dimensional (square-lattice) spin-1/2 quantum antiferromagnets using a numerical real-space renormalization-group (RG) approach. In our RG approach we consider blocks of various sizes but with an odd number of sites; we retain only the doublet ground state and we integrate out the higher-energy states by means of second-order quasidegenerate perturbation theory. That is, we assume that the role of the excited states of a block, in the RG iteration process, is to renormalize the effective coupling parameters between blocks. We compute the ground-state energy of a spin-1/2 linear chain for various block sizes and find close agreement with the Bethe-ansatz exact solution. In the case of the spin-1/2 square-lattice quantum antiferromagnet, the obtained ground-state energy is in reasonable agreement with the available numerical estimates.
Quantum groups, roots of unity and particles on quantized Anti-de Sitter space
Energy Technology Data Exchange (ETDEWEB)
Steinacker, Harold [Univ. of California, Berkeley, CA (United States). Dept. of Physics
1997-05-23
Quantum groups in general and the quantum Anti-de Sitter group U_{q}(so(2,3)) in particular are studied from the point of view of quantum field theory. The author shows that if q is a suitable root of unity, there exist finite-dimensional, unitary representations corresponding to essentially all the classical one-particle representations with (half) integer spin, with the same structure at low energies as in the classical case. In the massless case for spin ≥ 1, "naive" representations are unitarizable only after factoring out a subspace of "pure gauges", as classically. Unitary many-particle representations are defined, with the correct classical limit. Furthermore, the author identifies a remarkable element Q in the center of U_{q}(g), which plays the role of a BRST operator in the case of U_{q}(so(2,3)) at roots of unity, for any spin ≥ 1. The associated ghosts are an intrinsic part of the indecomposable representations. The author shows how to define an involution on algebras of creation and anihilation operators at roots of unity, in an example corresponding to non-identical particles. It is shown how nonabelian gauge fields appear naturally in this framework, without having to define connections on fiber bundles. Integration on Quantum Euclidean space and sphere and on Anti-de Sitter space is studied as well. The author gives a conjecture how Q can be used in general to analyze the structure of indecomposable representations, and to define a new, completely reducible associative (tensor) product of representations at roots of unity, which generalizes the standard "truncated" tensor product as well as many-particle representations.
Cellular distribution and cytotoxicity of graphene quantum dots with different functional groups
2014-01-01
Graphene quantum dots (GQDs) have been developed as promising optical probes for bioimaging due to their excellent photoluminescent properties. Additionally, the fluorescence spectrum and quantum yield of GQDs are highly dependent on the surface functional groups on the carbon sheets. However, the distribution and cytotoxicity of GQDs functionalized with different chemical groups have not been specifically investigated. Herein, the cytotoxicity of three kinds of GQDs with different modified groups (NH2, COOH, and CO-N (CH3)2, respectively) in human A549 lung carcinoma cells and human neural glioma C6 cells was investigated using thiazoyl blue colorimetric (MTT) assay and trypan blue assay. The cellular apoptosis or necrosis was then evaluated by flow cytometry analysis. It was demonstrated that the three modified GQDs showed good biocompatibility even when the concentration reached 200 μg/mL. The Raman spectra of cells treated with GQDs with different functional groups also showed no distinct changes, affording molecular level evidence for the biocompatibility of the three kinds of GQDs. The cellular distribution of the three modified GQDs was observed using a fluorescence microscope. The data revealed that GQDs randomly dispersed in the cytoplasm but not diffused into nucleus. Therefore, GQDs with different functional groups have low cytotoxicity and excellent biocompatibility regardless of chemical modification, offering good prospects for bioimaging and other biomedical applications. PMID:24597852
SU (2) lattice gauge theory simulations on Fermi GPUs
Cardoso, Nuno; Bicudo, Pedro
2011-05-01
In this work we explore the performance of CUDA in quenched lattice SU (2) simulations. CUDA, NVIDIA Compute Unified Device Architecture, is a hardware and software architecture developed by NVIDIA for computing on the GPU. We present an analysis and performance comparison between the GPU and CPU in single and double precision. Analyses with multiple GPUs and two different architectures (G200 and Fermi architectures) are also presented. In order to obtain a high performance, the code must be optimized for the GPU architecture, i.e., an implementation that exploits the memory hierarchy of the CUDA programming model. We produce codes for the Monte Carlo generation of SU (2) lattice gauge configurations, for the mean plaquette, for the Polyakov Loop at finite T and for the Wilson loop. We also present results for the potential using many configurations (50,000) without smearing and almost 2000 configurations with APE smearing. With two Fermi GPUs we have achieved an excellent performance of 200× the speed over one CPU, in single precision, around 110 Gflops/s. We also find that, using the Fermi architecture, double precision computations for the static quark-antiquark potential are not much slower (less than 2× slower) than single precision computations.
Al-Khalili, Jim
2003-01-01
In this lively look at quantum science, a physicist takes you on an entertaining and enlightening journey through the basics of subatomic physics. Along the way, he examines the paradox of quantum mechanics--beautifully mathematical in theory but confoundingly unpredictable in the real world. Marvel at the Dual Slit experiment as a tiny atom passes through two separate openings at the same time. Ponder the peculiar communication of quantum particles, which can remain in touch no matter how far apart. Join the genius jewel thief as he carries out a quantum measurement on a diamond without ever touching the object in question. Baffle yourself with the bizzareness of quantum tunneling, the equivalent of traveling partway up a hill, only to disappear then reappear traveling down the opposite side. With its clean, colorful layout and conversational tone, this text will hook you into the conundrum that is quantum mechanics.
Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group
Vian, F
1999-01-01
The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived f...
Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry
Directory of Open Access Journals (Sweden)
Chikashi Arita
2012-10-01
Full Text Available We study the entanglement properties of a higher-integer-spin Affleck-Kennedy-Lieb-Tasaki model with quantum group symmetry in the periodic boundary condition. We exactly calculate the finite size correction terms of the entanglement entropies from the double scaling limit. We also evaluate the geometric entanglement, which serves as another measure for entanglement. We find the geometric entanglement reaches its maximum at the isotropic point, and decreases with the increase of the anisotropy. This behavior is similar to that of the entanglement entropies.
Varchenko, A N
1995-01-01
This book recounts the connections between multidimensional hypergeometric functions and representation theory. In 1984, physicists Knizhnik and Zamolodchikov discovered a fundamental differential equation describing correlation functions in conformal field theory. The equation is defined in terms of a Lie algebra. Kohno and Drinfeld found that the monodromy of the differential equation is described in terms of the quantum group associated with the Lie algebra. It turns out that this phenomenon is the tip of the iceberg. The Knizhnik-Zamolodchikov differential equation is solved in multidimens
Irreversibility of the renormalization group flow in non-unitary quantum field theory
Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Ravanini, Francesco
2017-10-01
We show irreversibility of the renormalization group flow in non-unitary but {{ P}T} -invariant quantum field theory in two space-time dimensions. In addition to unbroken PT -symmetry and a positive energy spectrum, we assume standard properties of quantum field theory including a local energy-momentum tensor and relativistic invariance. This generalizes Zamolodchikov’s c-theorem to {{ P}T} -symmetric Hamiltonians. Our proof follows closely Zamolodchikov’s arguments. We show that a function ceff(s) of the renormalization group parameter s exists which is non-negative and monotonically decreasing along renormalization group flows. Its value at a critical point is the ‘effective central charge’ entering the specific free energy. At least in rational models, this equals ceff=c-24Δ , where c is the central charge and Δ is the lowest primary field dimension in the conformal field theory which describes the critical point. Dedicated to John Cardy on the occasion of his 70th birthday.
Gravitational leptogenesis in axion inflation with SU(2) gauge field
Maleknejad, Azadeh
2016-12-01
We present an intrinsic leptogenesis mechanism in models of axion inflation with a classical SU(2) gauge field. The gauge field is coupled to the axion with a Chern-Simons interaction and comprises a tiny fraction of the total energy, ρYM/ρtot lesssim epsilon2. However, it has spin-2 fluctuations which breaks the parity and leads to the generation of chiral gravitational waves during inflation. By the gravitational anomaly in SM, it naturally creates a net lepton number density, sufficient to explain the matter asymmetry. We show that this mechanism can generate the observed value of baryon to photon number density in a natural range of parameters and yet has a small chiral tensor power spectrum on large scales.
SU(2) Gauge Theory with Two Fundamental Flavours
DEFF Research Database (Denmark)
Arthur, Rudy; Drach, Vincent; Hansen, Martin
2016-01-01
(Goldstone) Higgs theories to several intriguing types of dark matter candidates, such as the SIMPs. We improve our previous lattice analysis [1] by adding more data at light quark masses, at two additional lattice spacings, by determining the lattice cutoff via a Wilson flow measure of the $w_0$ parameter......We investigate the continuum spectrum of the SU(2) gauge theory with $N_f=2$ flavours of fermions in the fundamental representation. This model provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics that range from composite......, and by measuring the relevant renormalisation constants non-perturbatively in the RI'-MOM scheme. Our results for the lightest isovector states in the vector and axial channels, in units of the pseudoscalar decay constant, are $m_V/F_{\\rm{PS}}\\sim 13.1(2.2)$ and $m_A/F_{\\rm{PS}}\\sim 14.5(3.6)$ (combining...
Dynamic SU(2) structure from seven-branes
Energy Technology Data Exchange (ETDEWEB)
Heidenreich, Ben; McAllister, Liam; /Cornell U., Phys. Dept.; Torroba, Gonzalo; /SLAC /Stanford U., Phys. Dept.
2010-12-16
We obtain a family of supersymmetric solutions of type IIB supergravity with dynamic SU(2) structure, which describe the local geometry near a stack of four D7-branes and one O7-plane wrapping a rigid four-cycle. The deformation to a generalized complex geometry is interpreted as a consequence of nonperturbative effects in the seven-brane gauge theory. We formulate the problem for seven-branes wrapping the base of an appropriate del Pezzo cone, and in the near-stack limit in which the four-cycle is flat, we obtain an exact solution in closed form. Our solutions serve to characterize the local geometry of nonperturbatively-stabilized flux compactifications.
Finite volume effects in SU(2) with two adjoint fermions
Patella, Agostino; Lucini, Biagio; Pica, Claudio; Rago, Antonio
2011-01-01
Many evidences from lattice simulations support the idea that SU(2) with two Dirac flavors in the adjoint representation (also called Minimal Walking Technicolor) is IR conformal. A possible way to see this is through the behavior of the spectrum of the mass-deformed theory. When fermions are massive, a mass-gap is generated and the theory is confined. IR-conformality is recovered in the chiral limit: masses of particles vanish in the chiral limit, while their ratios stay finite. In order to trust this analysis one has to relay on the infinite volume extrapolation. We will discuss the finite volume effects on the mesonic spectrum, investigated by varying the size of the lattice and by changing the boundary conditions for the fields.
Confinement from semiclassical gluon fields in SU(2) gauge theory
Langfeld, Kurt
2010-01-01
The infrared structure of SU(2) Yang-Mills theory is studied by means of lattice gauge simulations using a new constrained cooling technique. This method reduces the action while all Polyakov lines on the lattice remain unchanged. In contrast to unconstrained cooling, quark confinement is still intact. A study of the Hessian of the Yang-Mills action shows that low action (semi-) classical configurations can be achieved, with a characteristic splitting between collective modes and higher momentum modes. Besides confinement, the semiclassical configurations also support the topological susceptibility and generate spontaneous breakdown of chiral symmetry.We show that they possess a cluster structure of locally mainly (anti-) selfdual objects. By contrast to an instanton or a meron medium, the topological charge of individual clusters is smoothly distributed.
Operator coproduct-realization of quantum group transformations in two dimensional gravity, 1
Cremmer, E; Schnittger, J; Cremmer, E; Gervais, J L; Schnittger, J
1996-01-01
A simple connection between the universal R matrix of U_q(sl(2)) (for spins \\demi and J) and the required form of the co-product action of the Hilbert space generators of the quantum group symmetry is put forward. This gives an explicit operator realization of the co-product action on the covariant operators. It allows us to derive the quantum group covariance of the fusion and braiding matrices, although it is of a new type: the generators depend upon worldsheet variables, and obey a new central extension of U_q(sl(2)) realized by (what we call) fixed point commutation relations. This is explained by showing that the link between the algebra of field transformations and that of the co-product generators is much weaker than previously thought. The central charges of our extended U_q(sl(2)) algebra, which includes the Liouville zero-mode momentum in a nontrivial way are related to Virasoro-descendants of unity. We also show how our approach can be used to derive the Hopf algebra structure of the extended quant...
Progress gauge symmetry breaking in SU(6) x SU(2) sub R model
Hayashi, T; Matsuda, M; Matsuoka, T
2003-01-01
In the SU(6) x SU(2) sub R string-inspired model, we describe the evolution of the couplings and the masses down from the string scale M sub s using the renormalization group equations and minimize the effective potential. This model possesses the flavor symmetry, including the binary dihedral group D tilde sub 4. We show that the scalar mass squared of the gauge non-singlet matter field possibly becomes negative slightly below the string scale. As a consequence, the precocious radiative breaking of the gauge symmetry down to the standard model gauge group can be realized. In the present model, the large Yukawa coupling, which plays an important role in the symmetry breaking, is identical to the colored Higgs coupling related to the longevity of the proton. (author)
Fundamental fermion interactions via vector bosons of unified SU(2 x SU(4 gauge fields
Directory of Open Access Journals (Sweden)
Eckart eMarsch
2016-02-01
Full Text Available Employing the fermion unification model based on the intrinsic SU(8 symmetry of a generalized Dirac equation, we discuss the fundamental interactions under the SU(8=SU(2$otimes$SU(4 symmetry group. The physics involved can describe all fermions, the leptons (electron and neutrino, and the coloured up and down quarks of the first generation in the standard model (SM by a complex SU(8 octet of Dirac spinor fields. The fermion interactions are found to be mediated by the unified SU(4 and SU(2 vector gauge boson fields, which include the photon, the gluons, and the bosons $Z$ and $W$ as well known from the SM, but also comprise new ones, namely three coloured $X$ bosons carrying a fractional hypercharge of $pm4/3$ and transmuting leptons into quarks and vice versa. The full covariant derivative of the model is derived and discussed. The Higgs mechanism gives mass to the $Z$ and $W$ bosons, but also permits one to derive the mass of the coloured $X$ boson, for which depending on the choice of the values of the coupling constant, the estimates are 35~GeV or 156~GeV, values that are well within reach of the LHC. The scalar Higgs field can also lend masses to the fermions and fix their physical values for given appropriate coupling constants to that field.
Dynamical Generation of the Gauged SU(2) Linear Sigma Model
Delbourgo, R.; Scadron, M. D.
The fermion and meson sectors of the quark-level SU(2) linear sigma model are dynamically generated from a meson-quark Lagrangian, with the quark (q) and meson (σ, π) fields all treated as elementary, having neither bare masses nor expectation values. In the chiral limit, the masses are predicted to be mq = fπg, mπ = 0, mσ = 2mq, and we also find that the quark-meson coupling is g =2π /√ {Nc}, the three-meson coupling is g' =mσ 2 /2fπ =2gmq and the four-meson coupling is λ = 2g2 = g‧/fπ, where fπ ≃ 90 MeV is the pion decay constant and Nc = 3 is the color number. By gauging this model one can generate the couplings to the vector mesons ρ and A1, including the quark-vector coupling constant gρ = 2π, gρππ, gA1ρπ and the masses mρ 700 MeV, mA1˜= √ {3} mρ ; of course the vector and axial currents remain conserved throughout.
Type IIA orientifolds on SU(2)-structure manifolds
Energy Technology Data Exchange (ETDEWEB)
Danckaert, Thomas
2010-11-15
We investigate the possible supersymmetry-preserving orientifold projections of type IIA string theory on a six-dimensional background with SU(2)-structure. We find two categories of projections which preserve half of the low-energy supersymmetry, reducing the effective theory from an N=4 supergravity theory, to an N=2 supergravity. For these two cases, we impose the projection on the low-energy spectrum and reduce the effective N=4 supergravity action accordingly. We can identify the resulting gauged N=2 supergravity theory and bring the action into canonical form. We compute the scalar moduli spaces and characterize the gauged symmetries in terms of the geometry of these moduli spaces. Due to their origin in N=4 supergravity, which is a highly constrained theory, the moduli spaces are of a very simple form. We find that, for suitable background manifolds, isometries in all scalar sectors can become gauged. The obtained gaugings share many features with those of N=2 supergravities obtained previously from other G-structure compactifications. (orig.)
Quantum Games with Strategies Induced by Basis Change Rules
Frąckiewicz, Piotr; Pykacz, Jarosław
2017-12-01
The aim of the paper is to draw attention to a special class of two parameter unitary strategies in the Eisert-Wilkens-Lewenstein scheme for quantum games. We identify the players' strategies with basis change matrices. Then we prove that the resulting quantum game is invariant with respect to isomorphic transformations of the input game. Moreover, it is shown that the game so obtained may not be trivial with respect to pure Nash equilibria, compared with the model with strategies being the special unitary group SU(2).
Implementation of the SU(2) Hamiltonian symmetry for the DMRG algorithm
Alvarez, Gonzalo
2012-10-01
In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992, 1993) [1,2], Hamiltonian symmetries play an important rôle. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This paper explains how the the DMRG++ code (Alvarez, 2009) [3] has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries are discussed for the one-orbital Hubbard model, and for a two-orbital Hubbard model for iron-based superconductors. The computational bottleneck of the algorithm and the use of shared memory parallelization are also addressed. Program summary Program title: DMRG++ Catalog identifier: AEDJ_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDJ_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Special license. See http://cpc.cs.qub.ac.uk/licence/AEDJ_v2_0.html No. of lines in distributed program, including test data, etc.: 211560 No. of bytes in distributed program, including test data, etc.: 10572185 Distribution format: tar.gz Programming language: C++. Computer: PC. Operating system: Multiplatform, tested on Linux. Has the code been vectorized or parallelized?: Yes. 1 to 8 processors with MPI, 2 to 4 cores with pthreads. RAM: 1GB (256MB is enough to run the included test) Classification: 23. Catalog identifier of previous version: AEDJ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180(2009)1572 External routines: BLAS and LAPACK Nature of problem: Strongly correlated electrons systems, display a broad range of important phenomena, and their study is a major area of research in condensed matter physics. In this context, model Hamiltonians are used to simulate the relevant interactions of a given compound, and the relevant degrees of freedom. These studies
Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies
Energy Technology Data Exchange (ETDEWEB)
Groh, Kai
2012-10-15
The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement
Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations
Directory of Open Access Journals (Sweden)
Hitoshi Konno
2006-12-01
Full Text Available For any affine Lie algebra ${mathfrak g}$, we show that any finite dimensional representation of the universal dynamical $R$ matrix ${cal R}(lambda$ of the elliptic quantum group ${cal B}_{q,lambda}({mathfrak g}$ coincides with a corresponding connection matrix for the solutions of the $q$-KZ equation associated with $U_q({mathfrak g}$. This provides a general connection between ${cal B}_{q,lambda}({mathfrak g}$ and the elliptic face (IRF or SOS models. In particular, we construct vector representations of ${cal R}(lambda$ for ${mathfrak g}=A_n^{(1}$, $B_n^{(1}$, $C_n^{(1}$, $D_n^{(1}$, and show that they coincide with the face weights derived by Jimbo, Miwa and Okado. We hence confirm the conjecture by Frenkel and Reshetikhin.
Energy Technology Data Exchange (ETDEWEB)
Anders, Frithjof B [Institut fuer Theoretische Physik, Universitaet Bremen, PO Box 330 440, D-28334 Bremen (Germany)], E-mail: anders@itp.uni-bremen.de
2008-05-14
We present a method for the calculation of dynamical correlation functions of quantum impurity systems out of equilibrium using Wilson's numerical renormalization group (NRG). Our formulation is based on a complete basis set of the Wilson chain and embeds the recently derived algorithm for equilibrium spectral functions. Our method fulfils the spectral weight conserving sum-rule exactly by construction. A local Coulomb repulsion U>0 is switched on at t = 0, and the asymptotic steady-state spectral functions are obtained for various values of U as well as magnetic field strength H and temperature T. These benchmark tests show excellent agreement between the time-evolved and the directly calculated equilibrium NRG spectra for finite U. This method could be used for calculating steady-state non-equilibrium spectral functions at finite bias through interacting nanodevices.
Strong-disorder renormalization group study of aperiodic quantum Ising chains
Oliveira Filho, Fleury J.; Faria, Maicon S.; Vieira, André P.
2012-03-01
We employ an adaptation of a strong-disorder renormalization group technique in order to analyze the ferro-paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse field. In the presence of marginal or relevant geometric fluctuations induced by aperiodicity, for which the critical behavior is expected to depart from the Onsager universality class, we derive analytical and asymptotically exact expressions for various critical exponents (including the correlation length and the magnetization exponents, which are not easily obtainable by other methods), and shed light onto the nature of the ground-state structures in the neighborhood of the critical point. The main results obtained by this approach are confirmed by finite-size scaling analyses of numerical calculations based on the free-fermion method.
Quantum Criticality of Hot Random Spin Chains
Vasseur, R.; Potter, A. C.; Parameswaran, S. A.
2015-05-01
We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit nonergodic behavior at strong disorder. The analysis is conveniently implemented in terms of SU (2 )k anyon chains that include the Ising and Potts chains as notable examples. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states, leading us to dub them "quantum critical glasses." We argue that random-bond Heisenberg chains self-thermalize and that the excited-state entanglement crosses over from volume-law to logarithmic scaling at a length scale that diverges in the Heisenberg limit k →∞. The excited state fixed points are generically distinct from their ground state counterparts, and represent novel nonequilibrium critical phases of matter.
$b \\to s \\gamma$ Decay in $SU(2)_L \\times SU(2)_R \\times U(1)$ Extensions of the Standard Model
Cho, Peter; Misiak, Mikolaj
1993-01-01
The rare radiative decay $b \\to s \\gamma$ is studied in $SU(2)_L \\times SU(2)_R \\times U(1)$ extensions of the Standard Model. Matching conditions for coefficients of operators appearing in the low energy effective Hamiltonian for this process are derived, and QCD corrections to these coefficients are analyzed. The $b \\to s \\gamma$ decay rate is then calculated and compared with the corresponding Standard Model result. We find that observable deviations from Standard Model predictions can occ...
SO*(2N) coherent states for loop quantum gravity
Girelli, Florian; Sellaroli, Giuseppe
2017-07-01
A SU(2) intertwiner with N legs can be interpreted as the quantum state of a convex polyhedron with N faces (when working in 3D). We show that the intertwiner Hilbert space carries a representation of the non-compact group SO*(2 N ) . This group can be viewed as the subgroup of the symplectic group Sp(4 N ,R ) which preserves the SU(2) invariance. We construct the associated Perelomov coherent states and discuss the notion of semi-classical limit, which is more subtle than we could expect. Our work completes the work by Freidel and Livine [J. Math. Phys. 51, 082502 (2010) and J. Math. Phys. 52, 052502 (2011)], which focused on the U (N ) subgroup of SO*(2 N ) .
Extended Soliton Solutions in an Effective Action for SU(2 Yang-Mills Theory
Directory of Open Access Journals (Sweden)
Nobuyuki Sawado
2006-01-01
Full Text Available The Skyrme-Faddeev-Niemi (SFN model which is an O(3 σ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2 Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains an additional fourth-order term which destabilizes the soliton solution. We apply the perturbative treatment to the second derivative term in order to exclude (or reduce the ill behavior of the original action and show that the SFN model with the second derivative term possesses soliton solutions.
Couplings in D(2,1;α) superconformal mechanics from the SU(2) perspective
Energy Technology Data Exchange (ETDEWEB)
Galajinsky, Anton [Laboratory of Mathematical Physics, Tomsk Polytechnic University,Lenin Ave. 30, 634050 Tomsk (Russian Federation)
2017-03-09
Dynamical realizations of the most general N=4 superconformal group in one dimension D(2,1;α) are reconsidered from the perspective of the R-symmetry subgroup SU(2). It is shown that any realization of the R-symmetry subalgebra in some phase space can be extended to a representation of the Lie superalgebra corresponding to D(2,1;α). Novel couplings of arbitrary number of supermultiplets of the type (1,4,3) and (0,4,4) to a single supermultiplet of either the type (3,4,1), or (4,4,0) are constructed. D(2,1;α) superconformal mechanics describing superparticles propagating near the horizon of the extreme Reissner-Nordström-AdS-dS black hole in four and five dimensions is considered. The parameter α is linked to the cosmological constant.
Phase diagram of SU(2) with 2 flavors of dynamical adjoint quarks
Catterall, Simon; Sannino, Francesco; Schneible, Joe
2008-01-01
We report on numerical simulations of SU(2) lattice gauge theory with two flavors of light dynamical quarks in the adjoint of the gauge group. The dynamics of this theory is thought to be very different from QCD -- the theory exhibiting conformal or near conformal behavior in the infrared. We make a high resolution survey of the phase diagram of this model in the plane of the bare coupling and quark mass on lattices of size 8^3 \\times 16. Our simulations reveal a line of first order phase transitions extending from beta=0 to beta=beta_c \\sim 2.0. For beta > beta_c the line is no longer first order but continues as the locus of minimum meson mass. For beta > 2.0 we observe the critical pion and rho masses to be light, independent of bare coupling and approximately degenerate. We discuss possible interpretations of these observations and corresponding continuum limits.
Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group
Vian, F.
1999-05-01
The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived for the cutoff effective action at any momentum scale. Firstly the QAP is exploited to analyse the breaking of dilatation invariance occurring in the scalar theory in this approach. Then we address SU(N) Yang-Mills theory and extensively treat the key issue of the boundary conditions of the flow equation which, in this case, have also to ensure restoration of symmetry for the physical theory. In case of a chiral gauge theory, we show how the chiral anomaly can be obtained in the ERG. Finally, we extend the ERG formulation to supersymmetric (gauge) theories. It is emphasized regularization is implemented in such a way that supersymmetry is preserved.
Mee, J. K.; Raghunathan, R.; Murrell, D.; Braga, A.; Li, Y.; Lester, L. F.
2014-09-01
A detailed study of the pulse characteristics emitted from a monolithic Quantum Dot (QD) passively Mode-Locked Laser (MLL) has been performed using a state-of-the-art Frequency Resolved Optical Gating (FROG) pulse measurement system. While traditionally the time-domain pulse characteristics of semiconductor MLLs have been studied using digital sampling oscilloscope or intensity autocorrelation techniques, the FROG measurements allow for simultaneous characterization of time and frequency, which has been shown to be necessary and sufficient for true determination of mode-locked stability. In this paper, FROG pulse measurements are presented on a two-section QD MLL operating over wide temperature excursions. The FROG measurement allows for extraction of the temporal and spectral intensity and phase profiles from which the Group Delay Dispersion (GDD) can be determined. The magnitude of the GDD is found to decrease from 16.1 to 3.5 ps/nm when the temperature is increased from 20 to 50 oC, mirroring the trend of pulse width reduction at elevated temperature, which has been shown to correlate strongly with reduced unsaturated absorption. The possibility to further optimize pulse generation via intra-cavity dispersion compensation in a novel three-section MLL design is also examined, and shows strong potential toward providing valuable insight into the optimal cavity designs and operating parameters for QD MLLs.
Spin-anisotropy commensurable chains. Quantum group symmetries and N = 2 SUSY
Bérkovich, Alexander; Gómez, César; Sierra, Germán
1994-03-01
In this paper we consider a class of 2D integrable models. These models are higher- spin XXZ-chains with an extra condition of the commensurability between spin ( j) and anisotropy ( γ): sin γ (2 j + 1) = 0. Thus, the mathematics underlying this commensurability is provided by the quantum groups with the deformation parameter being an Nth root of unity. Our discussion covers a range of topics including new integrable deformations, thermodynamics, conformal behaviour, S-matrices and magnetization. The emerging picture strongly depends on the N-parity. For the N-even case at the commensurable point, S- matrices factorize into an N = 2 supersymmetric sine-Gordon matrix and an RSOS piece. The physics of the N-odd case is rather different. Here, there are hints suggesting that supersymmetry is still present, however we did not unravel its nature, yet. In this case, S-matrices factorize into two RSOS pieces. The second RSOS piece has dependence on an extra parameter. Away from the commensurable point, we find an unusual magnetic behaviour. The magnetization of our chains depends on the sign of the external magnetic field.
Real-Space Renormalization-Group Approach to the Integer Quantum Hall Effect
Cain, Philipp; Römer, Rudolf A.
We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, Pc(G), with very high accuracy. The RG flow of P(G) at energies away from the transition yields a value of the critical exponent ν that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as RL and RH is given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD). This distribution is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with ν = 2.37±0.02. Away from the transition it crosses over towards the Poisson distribution. We next investigate the plateau-to-insulator transition at strong magnetic fields. For a fully quantum coherent situation, we find a quantized Hall insulator with RH≈h/e2 up to RL 20h/e2 when interpreting the results in terms of most probable value of the distribution function P(RH). Upon further increasing RL→∞, the Hall insulator with diverging Hall resistance R H∝ R Lκ is seen. The crossover between these two regimes depends on the precise nature of the averaging procedure for the distributions P(RL) and P(RH). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition. Inhomogeneities are modeled by a smooth random potential with a correlator which falls off with distance as a power law r-α. Similar to the classical percolation, we observe an enhancement of ν with decreasing α. These results exemplify the surprising fact that a small RG unit, containing only five nodes, accurately captures most of the correlations responsible for the localization
Clark, Kevin B
2010-01-01
Learning to reciprocate socially valued actions, such as cheating and cooperation, marks evolutionary advances in animal intelligence thought unequalled by even colonial microbes known to secure respective individual or group fitness tradeoffs through genetic and epigenetic processes. However, solitary ciliates, unique among microbes for their emulation of simple Hebbian-like learning contingent upon feedback between behavioral output and vibration-activated mechanosensitive Ca(2+) channels, might be the best candidates to learn to reciprocate necessary preconjugant touches perceived during complex 'courtship rituals'. Testing this hypothesis here with mock social trials involving an ambiguous vibration source, the large heterotrich ciliate Spirostomum ambiguum showed it can indeed learn to modify emitted signals about mating fitness to encourage paired reproduction. Ciliates, improving their signaling expertise with each felt vibration, grouped serial escape strategies gesturing opposite 'courting' assurances of playing 'harder to get' or 'easier to get' into separate, topologically invariant computational networks. Stored strategies formed patterns of action or heuristics with which ciliates performed fast, quantum-like distributed modular searches to guide future replies of specific fitness content. Heuristic-guided searches helped initial inferior repliers, ciliates with high initial reproductive costs, learn to sensitize their behavioral output and opportunistically compete with presumptive mating 'rivals' advertising higher quality fitness. Whereas, initial superior repliers, ciliates with low initial reproductive costs, learned with the aid of heuristics to habituate their behavioral output and sacrifice net reproductive payoffs to cooperate with presumptive 'suitors', a kind of learned altruism only before attributed to animal social intelligences. The present findings confirm that ciliates are highly competent decision makers capable of achieving paired
Xu, Chao; Ban, Dayan
2016-06-13
The strategies and approaches of designing chirped Distributed Bragg Reflector for group velocity compensation in metal-metal waveguide terahertz quantum cascade laser are investigated through 1D and 3D models. The results show the depth of the corrugation periods plays an important role on achieving broad-band group velocity compensation in terahertz range. However, the deep corrugation also brings distortion to the group delay behavior. A two-section chirped DBR is proposed to provide smoother group delay compensation while still maintain the broad frequency range (octave) operation within 2 THz to 4 THz.
Liu, Shengyu; Zhang, Zhiqiang; Wang, Huifang
2012-01-01
Different reaction pathways of the carboxylic group in a brown coal model were investigated by applying density function quantum chemical theory, examining the possible cross-linking and decomposition reactions between the hydrogen bonded carboxylic group-carboxylic group and the carboxylic group-hydroxyl group during the thermal pyrolysis process. The results show that bimolecular dehydration and decarboxylation of hydrogen bonded carboxylic groups have distinctly lower activation barriers and therefore, proceed preferentially at low temperature. The esterification reaction between the hydrogen bonded carboxylic group and hydroxyl group, together with unimolecular decarboxylation of isolated single carboxylic groups were also possible at moderate temperature. Aryl-aryl coupling is thought to occur via radical pyrolysis and recombination at relatively high temperature.
The finite temperature phase transition in the lattice SU(2)-Higgs model
Farakos, K; Rummukainen, K; Shaposhnikov, Mikhail E
1994-01-01
We study the finite temperature transition of SU(2)-Higgs model with lattice Monte Carlo techniques. We use dimensional reduction to transform the original 4-dimensional SU(2)-gauge + fundamental Higgs theory to an effective 3-dimensional SU(2) + adjoint Higgs + fundamental Higgs model. The simulations were performed with Higgs masses of 35 and 80 GeV; in both cases we observe a stronger first order transition than the perturbation theory predicts, indicating that the dynamics of the transition strongly depend on non-perturbative effects.
Energy Technology Data Exchange (ETDEWEB)
Zinn-Justin, J
2003-08-01
In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)
Kondo physics in double quantum dot based Cooper pair splitters
Wrześniewski, Kacper; Weymann, Ireneusz
2017-11-01
The Andreev transport properties of double quantum dot based Cooper pair splitters with one superconducting and two normal leads are studied theoretically in the Kondo regime. The influence of the superconducting pairing correlations on the local density of states, Andreev transmission coefficient, and Cooper pair splitting efficiency is thoroughly analyzed. It is shown that finite superconducting pairing potential quickly suppresses the SU(2 ) Kondo effect, which can however reemerge for relatively large values of coupling to superconductor. In the SU(4 ) Kondo regime, a crossover from the SU(4 ) to the SU(2 ) Kondo state is found as the coupling to superconductor is enhanced. The analysis is performed by means of the density-matrix numerical renormalization group method.
Hidden U$_{q}$(sl(2)) x U$_{q}$(sl(2)) quantum group symmetry in two dimensional gravity
Cremmer, E; Schnittger, J
1997-01-01
In a previous paper, we proposed a construction of U_q(sl(2)) quantum group symmetry generators for 2d gravity, where we took the chiral vertex operators of the theory to be the quantum group covariant ones established in earlier works. The basic idea was that the covariant fields in the spin 1/2 representation themselves can be viewed as generators, as they act, by braiding, on the other fields exactly in the required way. Here we transform this construction to the more conventional description of 2d gravity in terms of Bloch wave/Coulomb gas vertex operators, thereby establishing for the first time its quantum group symmetry properties. A U_q(sl(2))\\otimes U_q(sl(2)) symmetry of a novel type emerges: The two Cartan-generator eigenvalues are specified by the choice of matrix element (bra/ket Verma-modules); the two Casimir eigenvalues are equal and specified by the Virasoro weight of the vertex operator considered; the co-product is defined with a matching condition dictated by the Hilbert space structure of...
Intertwining algebras of quantum superintegrable systems on the hyperboloid
Energy Technology Data Exchange (ETDEWEB)
Calzada, J A [Departamento de Matematica Aplicada, Escuela Superior de Ingenieros Industriales, Universidad de Valladolid, 47011 Valladolid (Spain); Kuru, S [Department of Physics, Faculty of Science, Ankara University, 06100 Ankara (Turkey); Negro, J; Olmo, M A del [Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid (Spain)], E-mail: juacal@eis.uva.es, E-mail: kuru@science.ankara.edu.tr, E-mail: jnegro@fta.uva.es, E-mail: olmo@fta.uva.es
2008-08-15
A class of quantum superintegrable Hamiltonians defined on a two-dimensional hyperboloid is considered together with a set of intertwining operators connecting all of them. It is shown that such intertwining operators close a su(2; 1) Lie algebra and determine the Hamiltonians through the Casimir operators. The physical states are characterized as unitary representations of su(2; 1)
Schatzl, Magdalena; Hackl, Florian; Glaser, Martin; Rauter, Patrick; Brehm, Moritz; Spindlberger, Lukas; Simbula, Angelica; Galli, Matteo; Fromherz, Thomas; Schäffler, Friedrich
2017-03-15
Efficient coupling to integrated high-quality-factor cavities is crucial for the employment of germanium quantum dot (QD) emitters in future monolithic silicon-based optoelectronic platforms. We report on strongly enhanced emission from single Ge QDs into L3 photonic crystal resonator (PCR) modes based on precise positioning of these dots at the maximum of the respective mode field energy density. Perfect site control of Ge QDs grown on prepatterned silicon-on-insulator substrates was exploited to fabricate in one processing run almost 300 PCRs containing single QDs in systematically varying positions within the cavities. Extensive photoluminescence studies on this cavity chip enable a direct evaluation of the position-dependent coupling efficiency between single dots and selected cavity modes. The experimental results demonstrate the great potential of the approach allowing CMOS-compatible parallel fabrication of arrays of spatially matched dot/cavity systems for group-IV-based data transfer or quantum optical systems in the telecom regime.
Quantum interaction of SU(1,1) Lie group with entangled a two 2-level atoms
Alqannas, Haifa S.; Khalil, E. M.
2018-01-01
In present contribution, we consider a two two-level atoms in non-resonance case interacting with a quantum system. The wave function is obtained via solving the Schrödinger equation. The initial density operator is assumed, with respect to the quantum system starts in a Barut-Girardello state. We use the numerical results to describe the entanglement between the subsystem. Some statistical aspects, the atomic inversion, the squeezing phenomena and negatively are discussed in details. We study the effective of the detuning parameter on the population inversion and the squeezing phenomenon. Finally the negativity for different values of the detuning parameter are examined. It is shown that the effects of the detuning parameter changes the region of the entanglement sudden death and sudden birth phenomena.
DEFF Research Database (Denmark)
Truelsen, Jimi Lee
2011-01-01
W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on PSL(2, )\\. Their result is quantitative in the sense that they find the precise asymptotics of the measure considered. We extend their result to Eisenstein series on , where is the ring of integers in...... in a totally real field of degree n over with narrow class number one, using the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on non-holomorphic Hilbert modular forms.......W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on PSL(2, )\\. Their result is quantitative in the sense that they find the precise asymptotics of the measure considered. We extend their result to Eisenstein series on , where is the ring of integers...
Role of quantum confinement in luminescence efficiency of group IV nanostructures
Energy Technology Data Exchange (ETDEWEB)
Barbagiovanni, E. G., E-mail: santino.gasparo@gmail.com [Laboratory for Simulation of Physical Systems, Beijing Computational Science Research Centre, Beijing 100084 (China); Lockwood, D. J.; Rowell, N. L. [Measurement Science and Standards, National Research Council, Ottawa, Ontario K1A 0R6 (Canada); Costa Filho, R. N. [Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará (Brazil); Berbezier, I.; Amiard, G.; Favre, L.; Ronda, A. [Institut Matériaux Microélectronique Nanosciences de Provence, UMR CNRS, 6137, Avenue Normandie Niemen, 13397 Marseille Cedex 20 (France); Faustini, M.; Grosso, D. [Laboratoire Chimie de la Matière Condensée de Paris, UMR-7574 UPMC-CNRS, Collège de France, 11, place Marcelin Berthelot, 75231 Paris (France)
2014-01-28
Experimental results obtained previously for the photoluminescence efficiency (PL{sub eff}) of Ge quantum dots (QDs) are theoretically studied. A log-log plot of PL{sub eff} versus QD diameter (D) resulted in an identical slope for each Ge QD sample only when E{sub G}∼(D{sup 2}+D){sup −1}. We identified that above D ≈ 6.2 nm: E{sub G}∼D{sup −1} due to a changing effective mass (EM), while below D ≈ 4.6 nm: E{sub G}∼D{sup −2} due to electron/hole confinement. We propose that as the QD size is initially reduced, the EM is reduced, which increases the Bohr radius and interface scattering until eventually pure quantum confinement effects dominate at small D.
DEFF Research Database (Denmark)
Truelsen, Jimi Lee
W. Luo and P. Sarnak have proved quantum unique ergodicity for Eisenstein series on $PSL(2,Z) \\backslash H$. We extend their result to Eisenstein series on $PSL(2,O) \\backslash H^n$, where $O$ is the ring of integers in a totally real field of degree $n$ over $Q$ with narrow class number one, usi...... the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on non-holomorphic Hilbert modular forms....
Noncommutative Riemannian geometry from quantum spacetime generated by twisted Poincaré group
Aguillón, Cesar A.; Much, Albert; Rosenbaum, Marcos; Vergara, J. David
2017-11-01
We investigate a quantum geometric space in the context of what could be considered an emerging effective theory from quantum gravity. Specifically we consider a two-parameter class of twisted Poincaré algebras, from which Lie-algebraic noncommutativities of the translations are derived as well as associative star-products, deformed Riemannian geometries, Lie-algebraic twisted Minkowski spaces, and quantum effects that arise as noncommutativities. Starting from a universal differential algebra of forms based on the above-mentioned Lie-algebraic noncommutativities of the translations, we construct the noncommutative differential forms and inner and outer derivations, which are the noncommutative equivalents of the vector fields in the case of commutative differential geometry. Having established the essentials of this formalism, we construct a bimodule, which is required to be central under the action of the inner derivations in order to have well-defined contractions and from where the algebraic dependence of its coefficients is derived. This again then defines the noncommutative equivalent of the geometrical line-element in commutative differential geometry. We stress, however, that even though the components of the twisted metric are by construction symmetric in their algebra valuation, it is not so for their inverse, and thus to construct it, we made use of Gel'fand's theory of quasi-determinants, which is conceptually straightforward but computationally quite complicated beyond an algebra of 3 generators. The consequences of the noncommutativity of the Lie-algebra twisted geometry are further discussed.
Multiconfigurational quantum propagation with trajectory-guided generalized coherent states.
Grigolo, Adriano; Viscondi, Thiago F; de Aguiar, Marcus A M
2016-03-07
A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring diversified physical properties, such as spin degrees of freedom or particle indistinguishability. The approach is illustrated with simple models for interacting bosons trapped in double- and triple-well potentials, most adequately described in terms of SU(2) and SU(3) bosonic coherent states, respectively.
Gutierrez, Mauricio; Brown, Kenneth
2015-03-01
Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code (QECC). It is common to model the noise as a depolarizing Pauli channel. However, it is not clear how sensitive a code's threshold is to the noise model, and whether or not a depolarizing channel is a good approximation for realistic errors. We have shown that, at the physical single-qubit level, efficient and more accurate approximations can be obtained. We now examine the feasibility of employing these approximations to obtain better estimates of a QECC's threshold. We calculate the level-1 pseudo-threshold for the Steane [[7,1,3
Evolution of Hall resistivity and spectral function with doping in the SU(2) theory of cuprates
Morice, C.; Montiel, X.; Pépin, C.
2017-10-01
Recent transport experiments in the cuprate superconductors linked the opening of the pseudogap to a change in electronic dispersion [S. Badoux et al., Nature (London) 531, 210 (2015), 10.1038/nature16983]. Transport measurements showed that the carrier density sharply changes from x to 1 +x at the pseudogap critical doping, in accordance with the change from Fermi arcs at low doping to a large hole Fermi surface at high doping. The SU(2) theory of cuprates shows that short-range antiferromagnetic correlations cause the arising of both charge and superconducting orders, which are related by an SU(2) symmetry. The fluctuations associated with this symmetry form a pseudogap phase. Here we derive the renormalized electronic propagator under the SU(2) dome, and calculate the spectral functions and transport quantities of the renormalized bands. We show that their evolution with doping matches both spectral and transport measurements.
Delgado, Francisco
2017-12-01
Quantum information processing should be generated through control of quantum evolution for physical systems being used as resources, such as superconducting circuits, spinspin couplings in ions and artificial anyons in electronic gases. They have a quantum dynamics which should be translated into more natural languages for quantum information processing. On this terrain, this language should let to establish manipulation operations on the associated quantum information states as classical information processing does. This work shows how a kind of processing operations can be settled and implemented for quantum states design and quantum processing for systems fulfilling a SU(2) reduction in their dynamics.
On the SU(2 vertical stroke 1) WZNW model and its statistical mechanics applications
Energy Technology Data Exchange (ETDEWEB)
Saleur, H. [CEA Centre d' Etudes de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[University of Southern California, Los Angeles, CA (United States). Dept. of Physics; Schomerus, V. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2006-11-15
Motivated by a careful analysis of the Laplacian on the supergroup SU(2 vertical stroke 1) we formulate a proposal for the state space of the SU(2 vertical stroke 1) WZNW model. We then use properties of sl(2 vertical stroke 1) characters to compute the partition function of the theory. In the special case of level k=1 the latter is found to agree with the properly regularized partition function for the continuum limit of the integrable sl(2 vertical stroke 1)3- anti 3 super-spin chain. Some general conclusions applicable to other WZNW models (in particular the case k=-1/2) are also drawn. (orig.)
Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study
DEFF Research Database (Denmark)
Zohar, Erez; Wahl, Thorsten B.; Burrello, Michele
2016-01-01
limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study...... of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation....
Li, Jian; Zhang, Baisheng; Zhang, Zhiqiang; Yan, Kefeng; Kang, Lixun
2014-12-01
The primary pyrolysis mechanisms of the sodium carboxylate group in sodium benzoate-used as a model compound of brown coal-were studied by performing quantum chemical computations using B3LYP and the CBS method. Various possible reaction pathways involving reactions such as unimolecular and bimolecular decarboxylation and decarbonylation, crosslinking, and radical attack in the brown coal matrix were explored. Without the participation of reactive radicals, unimolecular decarboxylation to release CO2 was calculated to be the most energetically favorable primary reaction pathway at the B3LYP/6-311+G (d, p) level of theory, and was also found to be more energetically favorable than decarboxylation of an carboxylic acid group. When CBS-QBS results were included, crosslinking between the sodium carboxylate group and the carboxylic acid and the decarboxylation of the sodium carboxylate group (catalyzed by the phenolic hydroxyl group) were found to be possible; this pathway competes with unimolecular decarboxylation of the sodium carboxylate group. Provided that H and CH3 radicals are present in the brown coal matrix and can access the sodium carboxylate group, accelerated pyrolysis of the sodium carboxylate group becomes feasible, leading to the release of an Na atom or an NaCO2 radical at the B3LYP/6-311+G (d, p) or CBS-QB3 level of theory, respectively.
Filippone, Michele; Mora, Christophe
2012-09-01
We formulate a general approach for studying the low-frequency response of an interacting quantum dot connected to leads in the presence of oscillating gate voltages. The energy dissipated is characterized by the charge relaxation resistance, which under the loose assumption of Fermi liquid behavior at low energy, is shown to depend only on static charge susceptibilities. The predictions of the scattering theory are recovered in the noninteracting limit while the effect of interactions is simply to replace densities of states by charge susceptibilities in formulas. In order to substantiate the Fermi liquid picture in the case of a quantum RC geometry, we apply a renormalization group analysis and derive the low-energy Hamiltonian for two specific models: the Anderson and the Coulomb blockade models. The Anderson model is shown, using a field theoretical approach based on Barnes slave bosons, to map onto the Kondo model. We recover the well-known expression of the Kondo temperature for the asymmetric Anderson model and compute the charge susceptibility. The Barnes slave bosons are extended to the Coulomb blockade model where the renormalization-group analysis can be carried out perturbatively up to zero energy. All calculations agree with the Fermi liquid nature of the low-energy fixed point and satisfy the Friedel sum rule.
Bernatowicz, Piotr
2015-10-01
Theory of nuclear spin-lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum effects are at stake, the relaxation behaviour of the nuclear spins in methyl groups is controlled by thermally activated classical jumps of the methyl group between its three orientations. The temperature effects on the relaxation rates can be modelled by Arrhenius behaviour of the correlation time of the jump process. The entire variety of relaxation effects in protonated methyl groups has recently been given a consistently quantum mechanical explanation not invoking the jump model regardless of the temperature range. It exploits the damped quantum rotation (DQR) theory originally developed to describe NMR line shape effects for hindered methyl groups. In the DQR model, the incoherent dynamics of the methyl group include two quantum rate, i.e., coherence-damping processes. For proton relaxation only one of these processes is relevant. In this paper, temperature-dependent proton spin-lattice relaxation data for the methyl groups in polycrystalline methyltriphenyl silane and methyltriphenyl germanium, both deuterated in aromatic positions, are reported and interpreted in terms of the DQR model. A comparison with the conventional approach exploiting the phenomenological Arrhenius equation is made. The present observations provide further indications that incoherent motions of molecular moieties in condensed phase can retain quantum character over much broad temperature range than is commonly thought.
Bernatowicz, Piotr; Shkurenko, Aleksander; Osior, Agnieszka; Kamieński, Bohdan; Szymański, Sławomir
2015-11-21
The theory of nuclear spin-lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum effects are at stake, the relaxation behaviour of the nuclear spins in methyl groups is controlled by thermally activated classical jumps of the methyl group between its three orientations. The temperature effects on the relaxation rates can be modelled by Arrhenius behaviour of the correlation time of the jump process. The entire variety of relaxation effects in protonated methyl groups have recently been given a consistent quantum mechanical explanation not invoking the jump model regardless of the temperature range. It exploits the damped quantum rotation (DQR) theory originally developed to describe NMR line shape effects for hindered methyl groups. In the DQR model, the incoherent dynamics of the methyl group include two quantum rate (i.e., coherence-damping) processes. For proton relaxation only one of these processes is relevant. In this paper, temperature-dependent proton spin-lattice relaxation data for the methyl groups in polycrystalline methyltriphenyl silane and methyltriphenyl germanium, both deuterated in aromatic positions, are reported and interpreted in terms of the DQR model. A comparison with the conventional approach exploiting the phenomenological Arrhenius equation is made. The present observations provide further indications that incoherent motions of molecular moieties in the condensed phase can retain quantum character over much broader temperature range than is commonly thought.
SU(2)$_{\\tiny\\mbox{CMB}}$ at high redshifts and the value of $H_0$
Hahn, Steffen
2016-01-01
We investigate a high-$z$ cosmological model to compute the co-moving sound horizon $r_s$ at baryon freeze-out following hydrogen recombination. This model assumes a replacement of the conventional CMB photon gas by SU(2) Yang-Mills thermodynamics, three flavors of massless neutrinos ($N_\
Supersymmetric solutions of SU(2-Fayet–Iliopoulos-gauged N=2, d=4 supergravity
Directory of Open Access Journals (Sweden)
Tomás Ortín
2017-03-01
Full Text Available We explore the construction of supersymmetric solutions of theories of N=2,d=4 supergravity with a SU(2 gauging and SU(2 Fayet–Iliopoulos terms. In these theories an SU(2 isometry subgroup of the Special-Kähler manifold is gauged together with a SU(2 R-symmetry subgroup. We construct several solutions of the CP‾3 quadratic model directly in four dimensions and of the ST[2,6] model by dimensional reduction of the solutions found by Cariglia and Mac Conamhna in N=(1,0,d=6 supergravity with the same kind of gauging. In the CP‾3 model, we construct an AdS2×S2 solution which is only 1/8 BPS and an R×H3 solutions that also preserves 1 of the 8 possible supersymmetries. We show how to use dimensional reduction as in the ungauged case to obtain Rn×Sm and also AdSn×Sm-type solutions (with different radii in 5- and 4-dimensions from the 6-dimensional AdS3×S3 solution.
Scattering lengths in SU(2) gauge theory with two fundamental fermions
DEFF Research Database (Denmark)
Arthur, R.; Drach, V.; Hansen, Martin Rasmus Lundquist
2014-01-01
We investigate non perturbatively scattering properties of Goldstone Bosons in an SU(2) gauge theory with two Wilson fermions in the fundamental representation. Such a theory can be used to build extensions of the Standard Model that unifies Technicolor and pseudo Goldstone composite Higgs models...
Mass anomalous dimension and running of the coupling in SU(2) with six fundamental fermions
DEFF Research Database (Denmark)
Bursa, Francis; Del Debbio, Luigi; Keegan, Liam
2010-01-01
We simulate SU(2) gauge theory with six massless fundamental Dirac fermions. By using the Schr\\"odinger Functional method we measure the running of the coupling and the fermion mass over a wide range of length scales. We observe very slow running of the coupling and construct an estimator for the...
Light Asymmetric Dark Matter on the Lattice: SU(2) Technicolor with Two Fundamental Flavors
DEFF Research Database (Denmark)
Lewis, Randy; Pica, Claudio; Sannino, Francesco
2012-01-01
The SU(2) gauge theory with two massless Dirac flavors constitutes the building block of several models of Technicolor. Furthermore it has also been used as a template for the construction of a natural light asymmetric, or mixed type, dark matter candidate. We use explicit lattice simulations to ...
Mass anomalous dimension of SU(2) using the spectral density method
Suorsa, Joni M; Rantaharju, Jarno; Rantalaiho, Teemu; Rummukainen, Kari; Tuominen, Kimmo; Tähtinen, Sara
2016-01-01
SU(2) with N_f = 6 and N_f = 8 are believed to have an infrared conformal fixed point. We use the spectral density method cross referenced with the mass step scaling method to evaluate the coupling constant dependence of the mass anomalous dimension for massless HEX smeared, clover improved Wilson fermions with Schr\\"odinger functional boundary conditions.
On 2D and 3D solitons in SU(2) gluo-dynamics
Energy Technology Data Exchange (ETDEWEB)
Bogolubskaya, Alla; Bogolubsky, Igor [Joint Institute for Nuclear Research - JINR, Joliot-Curie st., 6, Moskovskaya obl., 141980, Dubna (Russian Federation)
2010-07-01
We plan to indicate the possibility of soliton existence in 2D and 3D SU(2) gluo-dynamics. Hamiltonians in terms of radial functions will be presented. Localized in space field distributions which provide local minima to these Hamiltonians are studied. Their physical implications are discussed. (author)
Anatomy of isolated monopole in Abelian projection od SU(2) lattice gauge theory
Belavin, V A; Veselov, A I
2001-01-01
The structure of the isolated static monopolies in the maximum Abelian projection of the SU(2) gluodynamics on the lattice studied. The standard parametrization of the coupling matrix was used by determining the maximum Abelian projection of the R functional maximization relative to all scale transformations. The monopole radius R approx = 0.06 fm is evaluated
An SU(2) symmetry of the one-dimensional spin-1 XY model
Kitazawa, A; Nomura, K
2003-01-01
We show that the one-dimensional spin-1 XY model has an additional SU(2) symmetry for the open boundary condition and for an artificial one. We can explain some degeneracies of excitation states which were reported in previous numerical studies. (letter to the editor)
Gradient flow and IR fixed point in SU(2) with Nf=8 flavors
DEFF Research Database (Denmark)
Leino, Viljami; Karavirta, Tuomas; Rantaharju, Jarno
2015-01-01
We study the running of the coupling in SU(2) gauge theory with 8 massless fundamental representation fermion flavours, using the gradient flow method with the Schr\\"odinger functional boundary conditions. Gradient flow allows us to measure robust continuum limit for the step scaling function...
The gradient flow running coupling in SU2 with 8 flavors
DEFF Research Database (Denmark)
Rantaharju, Jarno; Karavirta, Tuomas; Leino, Viljami
2014-01-01
We present preliminary results of the gradient flow running coupling with Dirichlet boundary condition in the SU(2) gauge theory with 8 fermion flavours. Improvements to the gradient flow measurement allow us to obtain a robust continuum limit. The results are consistent with perturbative running...
Leontaris, George K
1999-01-01
In the context of the free-fermionic formulation of the heterotic superstring, we construct a three generation N=1 supersymmetric SU(4)xSU(2)LxSU(2)R model supplemented by an SU(8) hidden gauge symmetry and five Abelian factors. The symmetry breaking to the standard model is achieved using vacuum expectation values of a Higgs pair in (4bar,2R)+(4,2R) at a high scale. One linear combination of the Abelian symmetries is anomalous and is broken by vacuum expectation values of singlet fields along the flat directions of the superpotential. All consistent string vacua of the model are completely classified by solving the corresponding system of F- and D-flatness equations including non-renormalizable terms up to sixth order. The requirement of existence of electroweak massless doublets further restricts the phenomenologically viable vacua. The third generation fermions receive masses from the tree-level superpotential. Further, a complete calculation of all non-renormalizable fermion mass terms up to fifth order s...
Leontaris, George K
1999-01-01
In the context of the free-fermionic formulation of the heterotic superstring, we construct a three-generation N = 1 supersymmetric SU(4) x SU(2) sub L x SU(2) sub R model supplemented by an SU(8) hidden gauge symmetry and five Abelian factors. The symmetry breaking to the standard model is achieved using vacuum expectation values of a Higgs pair in (4,2 sub R) + (4-bar,2 sub R) at a high scale. One linear combination of the Abelian symmetries is anomalous and is broken by vacuum expectation values of singlet fields along the flat directions of the superpotential. All consistent string vacua of the model are completely classified by solving the corresponding system of F- and D-flatness equations including non-renormalizable terms up to sixth order. The requirement of existence of electroweak massless doublets imposes further restrictions to the phenomenologically viable vacua. The third generation fermions receive masses from the tree-level superpotential. Further, a complete calculation of all non-renormaliz...
New Hamiltonians for loop quantum cosmology with arbitrary spin representations
Ben Achour, Jibril; Brahma, Suddhasattwa; Geiller, Marc
2017-04-01
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the fundamental representation, and very little is known about the physics associated with higher spin labels. This constitutes an ambiguity of which the understanding, we believe, is fundamental for connecting loop quantum cosmology to full theories of quantum gravity like loop quantum gravity, its spin foam formulation, or cosmological group field theory. We take a step in this direction by providing here a new closed formula for the Hamiltonian of flat Friedmann-Lemaître-Robertson-Walker models regularized in a representation of arbitrary spin. This expression is furthermore polynomial in the basic variables which correspond to well-defined operators in the quantum theory, takes into account the so-called inverse-volume corrections, and treats in a unified way two different regularization schemes for the curvature. After studying the effective classical dynamics corresponding to single and multiple-spin Hamiltonians, we study the behavior of the critical density when the number of representations is increased and the stability of the difference equations in the quantum theory.
In(Ga)As quantum dot formation on group-III assisted catalyst-free InGaAs nanowires
Energy Technology Data Exchange (ETDEWEB)
Heiss, Martin; Ketterer, Bernt; Uccelli, Emanuele; Fontcuberta i Morral, Anna [Laboratoire des Materiaux Semiconducteurs, Institut des Materiaux, Ecole Polytechnique Federale de Lausanne (Switzerland); Ramon Morante, Joan [Departament d' Electronica, Universitat de Barcelona, E-08028 Barcelona, CAT (Spain); Arbiol, Jordi, E-mail: anna.fontcuberta-morral@epfl.ch [Institucio Catalana de Recerca i Estudis Avancats (ICREA) and Institut de Ciencia de Materials de Barcelona, CSIC, 08193 Bellaterra, CAT (Spain)
2011-05-13
Growth of GaAs and In{sub x}Ga{sub 1-x}As nanowires by the group-III assisted molecular beam epitaxy growth method on (001)GaAs/SiO{sub 2} substrates is studied in dependence on growth temperature, with the objective of maximizing the indium incorporation. Nanowire growth was achieved for growth temperatures as low as 550 deg. C. The incorporation of indium was studied by low temperature micro-photoluminescence spectroscopy, Raman spectroscopy and electron energy loss spectroscopy. The results show that the incorporation of indium achieved by lowering the growth temperature does not have the effect of increasing the indium concentration in the bulk of the nanowire, which is limited to 3-5%. For growth temperatures below 575 {sup 0}C, indium rich regions form at the surface of the nanowires as a consequence of the radial growth. This results in the formation of quantum dots, which exhibit spectrally narrow luminescence.
The integrable quantum group invariant A2n−1(2 and Dn+1(2 open spin chains
Directory of Open Access Journals (Sweden)
Rafael I. Nepomechie
2017-11-01
Full Text Available A family of A2n(2 integrable open spin chains with Uq(Cn symmetry was recently identified in arXiv:1702.01482. We identify here in a similar way a family of A2n−1(2 integrable open spin chains with Uq(Dn symmetry, and two families of Dn+1(2 integrable open spin chains with Uq(Bn symmetry. We discuss the consequences of these symmetries for the degeneracies and multiplicities of the spectrum. We propose Bethe ansatz solutions for two of these models, whose completeness we check numerically for small values of n and chain length N. We find formulas for the Dynkin labels in terms of the numbers of Bethe roots of each type, which are useful for determining the corresponding degeneracies. In an appendix, we briefly consider Dn+1(2 chains with other integrable boundary conditions, which do not have quantum group symmetry.
Energy Technology Data Exchange (ETDEWEB)
Weyer, Holger
2010-12-17
We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity. Insisting on a background independent nonperturbative renormalization group (RG) flow the coarse graining operation must be defined in terms of an unspecified variable metric since no rigid metric of a fixed background spacetime is available. This leads to an extra field dependence in the functional RG equation and a significantly different RG ow in comparison to the standard flow equation with a rigid metric in the mode cutoff. The background independent RG flow can possess a non-Gaussian fixed point, for instance, even though the corresponding standard one does not. We demonstrate the importance of this universal, essentially kinematical effect by computing the RG flow of Quantum Einstein Gravity (QEG) in the ''conformally reduced'' theory which discards all degrees of freedom contained in the metric except the conformal one. The conformally reduced Einstein-Hilbert approximation has exactly the same qualitative properties as in the full Einstein-Hilbert truncation. In particular it possesses the non-Gaussian fixed point which is necessary for asymptotic safety. Without the extra field dependence the resulting RG flow is that of a simple {phi}{sup 4}-theory. We employ the Local Potential Approximation for the conformal factor to generalize the RG flow on an infinite dimensional theory space. Again we find a Gaussian as well as a non-Gaussian fixed point which provides further evidence for the viability of the asymptotic safety scenario. The analog of the invariant cubic in the curvature which spoils perturbative renormalizability is seen to be unproblematic for the asymptotic safety of the conformally reduced theory. The scaling fields and dimensions of both fixed points are obtained explicitly and possible implications for the predictivity of the theory are discussed. Since the RG flow depends on the topology of the
Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study
Energy Technology Data Exchange (ETDEWEB)
Zohar, Erez, E-mail: erez.zohar@mpq.mpg.de [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching (Germany); Wahl, Thorsten B. [Rudolf Peierls Centre for Theoretical Physics, Oxford, 1 Keble Road, OX1 3NP (United Kingdom); Burrello, Michele, E-mail: michele.burrello@mpq.mpg.de [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching (Germany); Cirac, J. Ignacio [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching (Germany)
2016-11-15
Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.
Energy Technology Data Exchange (ETDEWEB)
Hue, L.T. [Duy Tan University, Institute of Research and Development, Da Nang City (Viet Nam); Vietnam Academy of Science and Technology, Institute of Physics, Hanoi (Viet Nam); Arbuzov, A.B. [Joint Institute for Nuclear Researches, Bogoliubov Laboratory for Theoretical Physics, Dubna (Russian Federation); Ngan, N.T.K. [Cantho University, Department of Physics, Cantho (Viet Nam); Vietnam Academy of Science and Technology, Graduate University of Science and Technology, Hanoi (Viet Nam); Long, H.N. [Ton Duc Thang University, Theoretical Particle Physics and Cosmology Research Group, Ho Chi Minh City (Viet Nam); Ton Duc Thang University, Faculty of Applied Sciences, Ho Chi Minh City (Viet Nam)
2017-05-15
The neutrino and Higgs sectors in the SU(2){sub 1} x SU(2){sub 2} x U(1){sub Y} model with lepton-flavor non-universality are discussed. We show that active neutrinos can get Majorana masses from radiative corrections, after adding only new singly charged Higgs bosons. The mechanism for the generation of neutrino masses is the same as in the Zee models. This also gives a hint to solving the dark matter problem based on similar ways discussed recently in many radiative neutrino mass models with dark matter. Except the active neutrinos, the appearance of singly charged Higgs bosons and dark matter does not affect significantly the physical spectrum of all particles in the original model. We indicate this point by investigating the Higgs sector in both cases before and after singly charged scalars are added into it. Many interesting properties of physical Higgs bosons, which were not shown previously, are explored. In particular, the mass matrices of charged and CP-odd Higgs fields are proportional to the coefficient of triple Higgs coupling μ. The mass eigenstates and eigenvalues in the CP-even Higgs sector are also presented. All couplings of the SM-like Higgs boson to normal fermions and gauge bosons are different from the SM predictions by a factor c{sub h}, which must satisfy the recent global fit of experimental data, namely 0.995 < vertical stroke c{sub h} vertical stroke < 1. We have analyzed a more general diagonalization of gauge boson mass matrices, then we show that the ratio of the tangents of the W-W{sup '} and Z-Z{sup '} mixing angles is exactly the cosine of the Weinberg angle, implying that number of parameters is reduced by 1. Signals of new physics from decays of new heavy fermions and Higgs bosons at LHC and constraints of their masses are also discussed. (orig.)
Hue, L. T.; Arbuzov, A. B.; Ngan, N. T. K.; Long, H. N.
2017-05-01
The neutrino and Higgs sectors in the { SU(2) }_1 × { SU(2) }_2 × { U(1) }_Y model with lepton-flavor non-universality are discussed. We show that active neutrinos can get Majorana masses from radiative corrections, after adding only new singly charged Higgs bosons. The mechanism for the generation of neutrino masses is the same as in the Zee models. This also gives a hint to solving the dark matter problem based on similar ways discussed recently in many radiative neutrino mass models with dark matter. Except the active neutrinos, the appearance of singly charged Higgs bosons and dark matter does not affect significantly the physical spectrum of all particles in the original model. We indicate this point by investigating the Higgs sector in both cases before and after singly charged scalars are added into it. Many interesting properties of physical Higgs bosons, which were not shown previously, are explored. In particular, the mass matrices of charged and CP-odd Higgs fields are proportional to the coefficient of triple Higgs coupling μ . The mass eigenstates and eigenvalues in the CP-even Higgs sector are also presented. All couplings of the SM-like Higgs boson to normal fermions and gauge bosons are different from the SM predictions by a factor c_h, which must satisfy the recent global fit of experimental data, namely 0.995Z-Z' mixing angles is exactly the cosine of the Weinberg angle, implying that number of parameters is reduced by 1. Signals of new physics from decays of new heavy fermions and Higgs bosons at LHC and constraints of their masses are also discussed.
From instantons to sphalerons: Time-dependent periodic solutions of SU(2)-Higgs theory
Energy Technology Data Exchange (ETDEWEB)
Frost, K.L.; Yaffe, L.G. [Department of Physics, University of Washington, Seattle, Washington 98105-1560 (United States)
1999-11-01
We solve numerically for periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. In the limit of short periods the solutions approach tiny instanton{endash}anti-instanton superpositions while, for longer periods, the solutions merge with the static sphaleron. A previously predicted bifurcation point, where two branches of periodic solutions meet, appears for Higgs boson masses larger than 3.091M{sub W}. {copyright} {ital 1999} {ital The American Physical Society}
Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics
Energy Technology Data Exchange (ETDEWEB)
Buividovich, P.V. [Joint Institute for Nuclear Research, Dubna (Russian Federation); Institute for Theoretical and Experimental Physics ITEP, Moscow (Russian Federation); Kalaydzhyan, T. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Institute for Theoretical and Experimental Physics ITEP, Moscow (Russian Federation); Polikarpov, M.I. [Institute for Theoretical and Experimental Physics ITEP, Moscow (Russian Federation)
2011-11-15
We study the effect of cooling on the spatial distribution of the topological charge density in quenched SU(2) lattice gauge theory with overlap fermions. We show that as the gauge field configurations are cooled, the Hausdorff dimension of regions where the topological charge is localized gradually changes from d=2/3 towards the total space dimension. Hence the cooling procedure destroys some of the essential properties of the topological charge distribution. (orig.)
First results for SU(2) Yang-Mills with one adjoint Dirac Fermion
Athenodorou, Andreas; Bergner, Georg; Lucini, Biagio; Patella, Agostino
2013-01-01
We present a first exploratory study of SU(2) gauge theory with one Dirac flavour in the adjoint representation. We provide initial results for the spectroscopy and the anomalous dimension for the chiral condensate. Our investigation indicates that the theory is conformal or near-conformal, with an anomalous dimension of order one. A discussion of the relevance of these findings in relation to walking technicolor scenarios is also presented.
Template Composite Dark Matter : SU(2) gauge theory with 2 fundamental flavours
Drach, Vincent; Pica, Claudio; Rantaharju, Jarno; Sannino, Francesco
2015-11-13
We present a non perturbative study of SU(2) gauge theory with two fundamental Dirac flavours. We discuss how the model can be used as a template for composite Dark Matter (DM). We estimate one particular interaction of the DM candidate with the Standard Model : the interaction through photon exchange computing the electric polarizability of the DM candidate. Finally, we briefly discuss the viability of the model given the present experimental constraints.
Topological quantum liquids with quaternion non-Abelian statistics.
Xu, Cenke; Ludwig, Andreas W W
2012-01-27
Noncollinear magnetic order is typically characterized by a tetrad ground state manifold (GSM) of three perpendicular vectors or nematic directors. We study three types of tetrad orders in two spatial dimensions, whose GSMs are SO(3) = S(3)/Z(2), S(3)/Z(4), and S(3)/Q(8), respectively. Q(8) denotes the non-Abelian quaternion group with eight elements. We demonstrate that after quantum disordering these three types of tetrad orders, the systems enter fully gapped liquid phases described by Z(2), Z(4), and non-Abelian quaternion gauge field theories, respectively. The latter case realizes Kitaev's non-Abelian toric code in terms of a rather simple spin-1 SU(2) quantum magnet. This non-Abelian topological phase possesses a 22-fold ground state degeneracy on the torus arising from the 22 representations of the Drinfeld double of Q(8).
Effect of SU(2) symmetry on many-body localization and thermalization
Protopopov, Ivan V.; Ho, Wen Wei; Abanin, Dmitry A.
2017-07-01
The many-body localized (MBL) phase is characterized by a complete set of quasilocal integrals of motion and area-law entanglement of excited eigenstates. We study the effect of non-Abelian continuous symmetries on MBL, considering the case of SU(2 ) symmetric disordered spin chains. The SU(2 ) symmetry imposes strong constraints on the entanglement structure of the eigenstates, precluding conventional MBL. We construct a fixed-point Hamiltonian, which realizes a nonergodic (but non-MBL) phase characterized by eigenstates having logarithmic scaling of entanglement with the system size, as well as an incomplete set of quasilocal integrals of motion. We study the response of such a phase to local symmetric perturbations, finding that even weak perturbations induce multispin resonances. We conclude that the nonergodic phase is generally unstable and that SU(2 ) symmetry implies thermalization. The approach introduced in this Rapid Communication can be used to study dynamics in disordered systems with non-Abelian symmetries, and provides a starting point for searching nonergodic phases beyond conventional MBL.
Vaezi, Mohammad-Sadegh; Vaezi, Abolhassan
2017-10-01
We study the concept of entanglement distance between two quantum states, which quantifies the amount of information shared between their reduced density matrices (RDMs). Using analytical arguments combined with density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we show that for gapless systems the entanglement distance has power law dependence on the energy separation and subsystem size, with αE and αℓ exponents, respectively. Using conformal field theory (CFT) we find αE=2 and αℓ=4 for Abelian theories with c =1 , as in the case of free fermions. For non-Abelian CFTs αE=0 , and αℓ is twice the conformal dimension of the thermal primary fields. For instance, for Z3 parafermion CFT αE=1 and αℓ=4 /5 . For gapped 1+1 dimensional (1+1D) fermion systems, we show that the entanglement distance divides the low energy excitations into two branches with different values of αE and αℓ. These two branches are related to momentum transfers near zero and π . We also demonstrate that the entanglement distance reaches its maximum for degenerate states related through nonlocal operators such as Wilson loops. For example, degenerate ground states (GSs) of 2+1D topological states have maximum entanglement distance. In contrast, degenerate GSs related through confined anyon excitations such as genons have minimum entanglement distance. Various implications of this concept for quantum simulations are discussed. Finally, based on the ideas developed we discuss the computational complexity of DMRG algorithms that are capable of finding all degenerate GSs.
{gamma} (2) modular symmetry, renormalization group flow and the quantum hall effect
Energy Technology Data Exchange (ETDEWEB)
Georgelin, Yvon [Groupe de Physique Theorique, Institut de Physique Nucleaire, Orsay (France); Masson, Thierry; Wallet, Jean-Christophe [Laboratoire de Physique Theorique (UMR 8627), Universitdede Paris-Sud, Orsay (France)
2000-01-14
We construct a family of holomorphic {beta}-functions whose renormalization group (RG) flow preserves the {gamma} (2) modular symmetry and reproduces the observed stability of the Hall plateaus. The semicircle law relating the longitudinal and Hall conductivities that has been experimentally observed is obtained from the integration of the RG equations for any permitted transition which can be identified from the selection rules encoded in the flow diagram. The generic scale dependence of the conductivities is found to agree qualitatively with the present experimental data. The existence of a crossing point occurring in the crossover of the permitted transitions is discussed. (author)
Energy Technology Data Exchange (ETDEWEB)
Hu, Zi-Xiang, E-mail: zihu@princeton.edu [Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 (United States); Department of Physics, ChongQing University, ChongQing 400044 (China); Papić, Z.; Johri, S.; Bhatt, R.N. [Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 (United States); Schmitteckert, Peter [Institut für Nanotechnologie, Forschungszentrum Karlsruhe, D-76021 Karlsruhe (Germany)
2012-06-18
We report a systematic study of the fractional quantum Hall effect (FQHE) using the density-matrix renormalization group (DMRG) method on two different geometries: the sphere and the cylinder. We provide convergence benchmarks based on model Hamiltonians known to possess exact zero-energy ground states, as well as an analysis of the number of sweeps and basis elements that need to be kept in order to achieve the desired accuracy. The ground state energies of the Coulomb Hamiltonian at ν=1/3 and ν=5/2 filling are extracted and compared with the results obtained by previous DMRG implementations in the literature. A remarkably rapid convergence in the cylinder geometry is noted and suggests that this boundary condition is particularly suited for the application of the DMRG method to the FQHE. -- Highlights: ► FQHE is a two-dimensional physics. ► Density-matrix renormalization group method applied to FQH systems. ► Benchmark study both on sphere and cylinder geometry.
Pearsall, Thomas P
2017-01-01
This textbook employs a pedagogical approach that facilitates access to the fundamentals of Quantum Photonics. It contains an introductory description of the quantum properties of photons through the second quantization of the electromagnetic field, introducing stimulated and spontaneous emission of photons at the quantum level. Schrödinger’s equation is used to describe the behavior of electrons in a one-dimensional potential. Tunneling through a barrier is used to introduce the concept of nonlocality of an electron at the quantum level, which is closely-related to quantum confinement tunneling, resonant tunneling, and the origin of energy bands in both periodic (crystalline) and aperiodic (non-crystalline) materials. Introducing the concepts of reciprocal space, Brillouin zones, and Bloch’s theorem, the determination of electronic band structure using the pseudopotential method is presented, allowing direct computation of the band structures of most group IV, group III-V, and group II-VI semiconducto...
Aspects of finite field-dependent symmetry in SU(2) Cho–Faddeev–Niemi decomposition
Energy Technology Data Exchange (ETDEWEB)
Upadhyay, Sudhaker, E-mail: sudhakerupadhyay@gmail.com
2013-11-25
In this Letter we consider SU(2) Yang–Mills theory analyzed in Cho–Faddeev–Niemi variables which remains invariant under local gauge transformations. The BRST symmetries of this theory are generalized by making the infinitesimal parameter finite and field-dependent. Further, we show that under appropriate choices of finite and field-dependent parameter, the gauge-fixing and ghost terms corresponding to Landau as well as maximal Abelian gauge for such Cho–Faddeev–Niemi decomposed theory appear naturally within functional integral through Jacobian calculation.
Topology in SU(2) lattice gauge theory and parallelization of functional magnetic resonance imaging
Energy Technology Data Exchange (ETDEWEB)
Solbrig, Stefan
2008-07-01
In this thesis, I discuss topological properties of quenched SU(2) lattice gauge fields. In particular, clusters of topological charge density exhibit a power-law. The exponent of that power-law can be used to validate models for lattice gauge fields. Instead of working with fixed cutoffs of the topological charge density, using the notion of a ''watermark'' is more convenient. Furthermore, I discuss how a parallel computer, originally designed for lattice gauge field simulations, can be used for functional magnetic resonance imaging. Multi parameter fits can be parallelized to achieve almost real-time evaluation of fMRI data. (orig.)
Spherically symmetric classical solutions in SU(2) gauge theory with a Higgs field
Energy Technology Data Exchange (ETDEWEB)
Ratra, B.; Yaffe, L.G.
1988-04-21
A consistent ansatz for time dependent classical solutions in an SU(2) gauge theory with a doublet Higgs field is presented. The (3+1)-dimensional field equations are reduced to those of an effective (1+1)-dimensional theory. This ansatz describes solutions which travel between topologically distinct classical vacua of the non-abelian gauge theory. The real time version of these solutions describes the creation and decay of the unstable static 'sphaleron', the imaginary time version describes a euclidean instanton. (orig.)
Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory
Wetzel, Sebastian J.; Scherzer, Manuel
2017-11-01
We present a solution to the problem of interpreting neural networks classifying phases of matter. We devise a procedure for reconstructing the decision function of an artificial neural network as a simple function of the input, provided the decision function is sufficiently symmetric. In this case one can easily deduce the quantity by which the neural network classifies the input. The method is applied to the Ising model and SU(2) lattice gauge theory. In both systems we deduce the explicit expressions of the order parameters from the decision functions of the neural networks. We assume no prior knowledge about the Hamiltonian or the order parameters except Monte Carlo-sampled configurations.
Representations of the deformed U(su(2)) and U(osp(1,2)) algebras
Bonatsos, Dennis; Kolokotronis, P; Lenis, D; Bonatsos, Dennis
1996-01-01
The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are based on the construction of Verma modules, which are quotient modules, generated by ideals of the original algebra. This construction unifies a large number of the known algebras under the same scheme. The finite dimensional representations show new features such as the multiplicity of representations of the same dimensionality, or the existence of finite dimensional representations only for some dimensions.
From decay to complete breaking: pulling the strings in SU(2) Yang-Mills theory.
Pepe, M; Wiese, U-J
2009-05-15
We study {2Q+1} strings connecting two static charges Q in (2+1)D SU(2) Yang-Mills theory. While the fundamental {2} string between two charges Q=1/2 is unbreakable, the adjoint {3} string connecting two charges Q=1 can break. When a {4} string is stretched beyond a critical length, it decays into a {2} string by gluon pair creation. When a {5} string is stretched, it first decays into a {3} string, which eventually breaks completely. The energy of the screened charges at the ends of a string is well described by a phenomenological constituent gluon model.
Monopoles in the Plaquette Formulation of the 3D SU(2) Lattice Gauge Theory
Borisenko, O; Boháčik, J
2011-01-01
Using a plaquette formulation for lattice gauge models we describe monopoles of the three dimensional SU(2) theory which appear as configurations in the complete axial gauge and violate the continuum Bianchi identity. Furthemore we derive a dual formulation for the Wilson loop in arbitrary representation and calculate the form of the interaction between generated electric flux and monopoles in the region of a weak coupling relevant for the continuum limit. The effective theory which controls the interaction is of the sine-Gordon type model. The string tension is calculated within the semiclassical approximation.
Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
Caselle, Michele; Panero, Marco
2015-01-01
We present a high-precision lattice calculation of the equation of state in the confining phase of SU(2) Yang-Mills theory. We show that the results are described very well by a gas of massive, non-interacting glueballs, provided one assumes an exponentially growing Hagedorn spectrum. The latter can be derived within an effective bosonic closed-string model, leading to a parameter-free theoretical prediction, which is in perfect agreement with our lattice results. Furthermore, when applied to SU(3) Yang-Mills theory, this effective model accurately describes the lattice results reported by Bors\\'anyi et al. in JHEP 07 (2012) 056.
Correlation functions of the energy-momentum tensor in SU(2) gauge theory at finite temperature
DEFF Research Database (Denmark)
Huebner, K.; Karsch, F.; Pica, Claudio
2008-01-01
We calculate correlation functions of the energy-momentum tensor in the vicinity of the deconfinement phase transition of (3+1)-dimensional SU(2) gauge theory and discuss their critical behavior in the vicinity of the second order deconfinement transition. We show that correlation functions...... of the trace of the energy momentum tensor diverge uniformly at the critical point in proportion to the specific heat singularity. Correlation functions of the pressure, on the other hand, stay finite at the critical point. We discuss the consequences of these findings for the analysis of transport...
An Exact SU(2) Symmetry and Persistent Spin Helix in a Spin-Orbit Coupled System
Energy Technology Data Exchange (ETDEWEB)
Bernevig, Andrei
2010-02-10
Spin-orbit coupled systems generally break the spin rotation symmetry. However, for a model with equal Rashba and Dresselhauss coupling constant (the ReD model), and for the [110] Dresselhauss model, a new type of SU(2) spin rotation symmetry is discovered. This symmetry is robust against spin-independent disorder and interactions, and is generated by operators whose wavevector depends on the coupling strength. It renders the spin lifetime infinite at this wavevector, giving rise to a Persistent Spin Helix (PSH). We obtain the spin fluctuation dynamics at, and away, from the symmetry point, and suggest experiments to observe the PSH.
An Exact SU(2) Symmetry and Persistent Spin Helix ina Spin-orbit Coupled System
Energy Technology Data Exchange (ETDEWEB)
Bernevig, B.A.; /Stanford U., Phys. Dept. /Santa Barbara, KITP; Orenstein, J.; /LBL, Berkeley /UC, Berkeley; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2007-01-22
Spin-orbit coupled systems generally break the spin rotation symmetry. However, for a model with equal Rashba and Dresselhauss coupling constant (the ReD model), and for the [110] Dresselhauss model, a new type of SU(2) spin rotation symmetry is discovered. This symmetry is robust against spin-independent disorder and interactions, and is generated by operators whose wavevector depends on the coupling strength. It renders the spin lifetime infinite at this wavevector, giving rise to a Persistent Spin Helix (PSH). We obtain the spin fluctuation dynamics at, and away, from the symmetry point, and suggest experiments to observe the PSH.
Infrared conformality and bulk critical points: SU(2) with heavy adjoint quarks
Lucini, Biagio; Rago, Antonio; Rinaldi, Enrico
2013-01-01
The lattice phase structure of a gauge theory can be a serious obstruction to Monte Carlo studies of its continuum behaviour. This issue is particularly delicate when numerical studies are performed to determine whether a theory is in a (near-)conformal phase. In this work we investigate the heavy mass limit of the SU(2) gauge theory with Nf=2 adjoint fermions and its lattice phase diagram, showing the presence of a critical point ending a line of first order bulk phase transition. The relevant gauge observables and the low-lying spectrum are monitored in the vicinity of the critical point with very good control over different systematic effects. The scaling properties of masses and susceptibilities open the possibility that the effective theory at criticality is a scalar theory in the universality class of the four-dimensional Gaussian model. This behaviour is clearly different from what is observed for SU(2) gauge theory with two dynamical adjoint fermions, whose (near-)conformal numerical signature is henc...
More on the SU(2) deconfinement transition in the mixed action
Energy Technology Data Exchange (ETDEWEB)
Gavai, R.V. [Theoretical Physics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005 (India); Mathur, M. [Dipartimento di Fisica dell Universita and INFN, Piazza Torricelli 2 Pisa-56100 (Italy)
1997-07-01
We examine certain issues related to the universality of the SU(2) lattice gauge theory at nonzero temperatures. Using Monte Carlo simulations and strong coupling expansions, we study the behavior of the deconfinement transition in an extended coupling plane ({beta},{beta}{sub A}) around the tricritical point where the deconfinement transition changes from second to first order. Our numerical results on N{sub {tau}}=2,4,6,8 lattices show that the tricritical point first moves down towards the Wilson axis and then moves slowly upwards, if at all, as the lattice spacing is reduced. Lattices with very large N{sub {tau}} seem to be, therefore, necessary for the mixed action to exhibit the critical exponents of the three-dimensional Ising model for positive values of the adjoint coupling. {copyright} {ital 1997} {ital The American Physical Society}
Kramers-Wannier duality and worldline representation for the SU(2) principal chiral model
Gattringer, Christof; Göschl, Daniel; Marchis, Carlotta
2018-03-01
In this letter we explore different representations of the SU(2) principal chiral model on the lattice. We couple chemical potentials to two of the conserved charges to induce finite density. This leads to a complex action such that the conventional field representation cannot be used for a Monte Carlo simulation. Using the recently developed Abelian color flux approach we derive a new worldline representation where the partition sum has only real and positive weights, such that a Monte Carlo simulation is possible. In a second step we transform the model to new dual variables in the Kramers-Wannier (KW) sense, such that the constraints are automatically fulfilled, and we obtain a second representation free of the complex action problem. We implement exploratory Monte Carlo simulations for both, the worldline, as well as the KW-dual form, for cross-checking the two dualizations and a first assessment of their potential for dual simulations.
Rho meson decay width in SU(2) gauge theories with 2 fundamental flavours
Janowski, Tadeusz; Pica, Claudio
2016-01-01
SU(2) gauge theories with two quark flavours in the fundamental representation are among the most promising theories of composite dynamics describing the electroweak sector. Three out of five Goldstone bosons in these models become the longitudinal components of the W and Z bosons giving them mass. Like in QCD, we expect a spectrum of excitations which appear as resonances in vector boson scattering, in particular the vector resonance corresponding to the rho-meson in QCD. In this talk I will present the preliminary results of the first calculation of the rho-meson decay width in this theory, which is analogous to rho to two pions decay calculation in QCD. The results presented were calculated in a moving frame with total momentum (0,0,1) on two ensembles. Future plans include using 3 moving frames on a larger set of ensembles to extract the resonance parameters more reliably and also take the chiral and continuum limits.
$SU(2)$ gauge theory with two fundamental flavours: scalar and pseudoscalar spectrum
Arthur, Rudy; Hietanen, Ari; Pica, Claudio; Sannino, Francesco
2016-01-01
We investigate the scalar and pseudoscalar spectrum of the $SU(2)$ gauge theory with $N_f=2$ flavours of fermions in the fundamental representation using non perturbative lattice simulations. We provide first benchmark estimates of the mass of the lightest $0(0^{+})$ ($\\sigma$), $0(0^{-})$ ($\\eta'$) and $1(0^+)$ ($a_0$) states, including estimates of the relevant disconnected contributions. We find $m_{a_0}/F_{\\rm{PS}}= 16.7(4.9)$, $m_\\sigma/F_{\\rm{PS}}=19.2(10.8)$ and $m_{\\eta'}/F_{\\rm{PS}} = 12.8(4.7)$. These values for the masses of light scalar states provide crucial information for composite extensions of the Standard Model from the unified Fundamental Composi te Higgs-Technicolor theory \\cite{Cacciapaglia:2014uja} to models of composite dark matter.
Study of shear viscosity of SU(2)-gluodynamics within lattice simulation
Energy Technology Data Exchange (ETDEWEB)
Astrakhantsev, N.Yu. [Institute for Theoretical and Experimental Physics,Moscow, 117218 (Russian Federation); Moscow Institute of Physics and Technology,Dolgoprudny, 141700 (Russian Federation); Braguta, V.V. [Institute for Theoretical and Experimental Physics,Moscow, 117218 (Russian Federation); Institute for High Energy Physics NRC “Kurchatov Institute”,Protvino, 142281 Russian Federation (Russian Federation); Far Eastern Federal University, School of Biomedicine,Vladivostok, 690950 (Russian Federation); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute),Kashirskoe highway, 31, Moscow, 115409 (Russian Federation); Kotov, A.Yu. [Institute for Theoretical and Experimental Physics,Moscow, 117218 (Russian Federation); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute),Kashirskoe highway, 31, Moscow, 115409 (Russian Federation)
2015-09-14
This paper is devoted to the study of two-point correlation function of the energy-momentum tensor 〈T{sub 12}T{sub 12}〉 for SU(2)-gluodynamics within lattice simulation of QCD. Using multilevel algorithm we carried out the measurement of the correlation function at the temperature T/T{sub c}≃1.2. It is shown that lattice data can be described by spectral functions which interpolate between hydrodynamics at low frequencies and asymptotic freedom at high frequencies. The results of the study of spectral functions allowed us to estimate the ratio of shear viscosity to the entropy density η/s=0.134±0.057.
Scaling properties of SU(2) gauge theory with mixed fundamental-adjoint action
Rinaldi, Enrico; Lucini, Biagio; Patella, Agostino; Rago, Antonio
2012-01-01
We study the phase diagram of the SU(2) lattice gauge theory with fundamental-adjoint Wilson plaquette action. We confirm the presence of a first order bulk phase transition and we estimate the location of its end-point in the bare parameter space. If this point is second order, the theory is one of the simplest realizations of a lattice gauge theory admitting a continuum limit at finite bare couplings. All the relevant gauge observables are monitored in the vicinity of the fixed point with very good control over finite-size effects. The scaling properties of the low-lying glueball spectrum are studied while approaching the end-point in a controlled manner.
Confining vs. conformal scenario for SU(2) with adjoint fermions. Gluonic observables
Patella, Agostino; Lucini, Biagio; Pica, Claudio; Rago, Antonio
2010-01-01
Walking technicolor is a mechanism for electroweak symmetry breaking without Higgs field. The Higgs mechanism is provided by chiral symmetry breaking in the technicolor theory. An essential ingredient is the vicinity to an IR fixed point, which could reconcile technicolor with the electroweak precision tests. SU(2) gauge theory with two Dirac adjoint fermions has been proposed as a candidate for walking technicolor. Understanding whether this theory is confining or IR-conformal is a challenging problem, which can be addressed by means of numerical simulations. We have pointed out that a clean signal for the existence of an IR fixed point in this theory can be obtained by comparing the mesonic and gluonic sectors. We review some technical details of our calculations. Possible systematic errors are discussed.
Supersymmetric Extension of Non-Hermitian su(2 Hamiltonian and Supercoherent States
Directory of Open Access Journals (Sweden)
Omar Cherbal
2010-12-01
Full Text Available A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2 generators in the form H=ωJ_3+αJ_−+βJ_+, α≠β, is analyzed. The metrics which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is performed. They correspond to the pseudo-Hermitian supersymmetric systems of the boson-phermion oscillators. We extend the supercoherent states formalism to such supersymmetic systems via the pseudo-unitary supersymmetric displacement operator method. The constructed family of these supercoherent states consists of two dual subfamilies that form a bi-overcomplete and bi-normal system in the boson-phermion Fock space. The states of each subfamily are eigenvectors of the boson annihilation operator and of one of the two phermion lowering operators.
Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
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Caselle, Michele; Nada, Alessandro; Panero, Marco [Department of Physics, University of Turin & INFN,Via Pietro Giuria 1, I-10125 Turin (Italy)
2015-07-27
We present a high-precision lattice calculation of the equation of state in the confining phase of SU(2) Yang-Mills theory. We show that the results are described very well by a gas of massive, non-interacting glueballs, provided one assumes an exponentially growing Hagedorn spectrum. The latter can be derived within an effective bosonic closed-string model, leading to a parameter-free theoretical prediction, which is in perfect agreement with our lattice results. Furthermore, when applied to SU(3) Yang-Mills theory, this effective model accurately describes the lattice results reported by Borsányi et al. in http://dx.doi.org/10.1007/JHEP07(2012)056.
SU(2)CMB at high redshifts and the value of H0
Hahn, Steffen; Hofmann, Ralf
2017-07-01
We investigate a high-z cosmological model to compute the comoving sound horizon rs at baryon-velocity freeze-out towards the end of hydrogen recombination. This model assumes a replacement of the conventional cosmic microwave background (CMB) photon gas by deconfining SU(2) Yang-Mills thermodynamics, three flavours of massless neutrinos (Nν = 3) and a purely baryonic matter sector [no cold dark-matter (CDM)]. The according SU(2) temperature-redshift relation of the CMB is contrasted with recent measurements appealing to the thermal Sunyaev-Zel'dovich effect and CMB-photon absorption by molecular rotation bands or atomic hyperfine levels. Relying on a realistic simulation of the ionization history throughout recombination, we obtain z* = 1693.55 ± 6.98 and zdrag = 1812.66 ± 7.01. Due to considerable widths of the visibility functions in the solutions to the associated Boltzmann hierarchy and Euler equation, we conclude that z* and zdrag overestimate the redshifts for the respective photon and baryon-velocity freeze-out. Realistic decoupling values turn out to be zlf,* = 1554.89 ± 5.18 and zlf, drag = 1659.30 ± 5.48. With rs(zlf, drag) = (137.19 ± 0.45) Mpc and the essentially model independent extraction of rsH0 = constant from low-z data in Bernal, Verde & Riess, we obtain a good match with the value H0 = (73.24 ± 1.74) km s-1 Mpc-1 extracted in Riess et al. by appealing to Cepheid-calibrated Type Ia supernovae, new parallax measurements, stronger constraints on the Hubble flow and a refined computation of distance to NGC 4258 from maser data. We briefly comment on a possible interpolation of our high-z model, invoking percolated and unpercolated U(1) topological solitons of a Planck-scale axion field, to the phenomenologically successful low-z ΛCDM cosmology.
Directory of Open Access Journals (Sweden)
Vita Solomko
2016-01-01
Full Text Available The energetic structures and conformations of trimethine cyanine dye molecules were investigated. For research, group theoretical and quantum chemical calculation methods were used. The theoretical group analysis of electronic and vibrational structure of molecules was carried out. Also, the energetic structures and conformations of the molecule of this dye were studied. Research shows that the investigated molecule may reside in three different conformational states, one of which is highly symmetric (symmetry C2v and the other two with low symmetry. The third conformer is characterized by lowering of binding energy of the electronic system by 0.23 eV, and the long-wavelength absorption band is shifted to lower energies. Also the group theoretical analysis of the trimethine cyanine molecule had allowed systematizing the vibrational and electronic quantum transitions and identifying the bands in the absorption spectra. It is shown that the excitation of the molecule in S1-state causes trans-cis-isomerization. The presence of the barrier of ~0.1 eV allows the fluorescence process to compete with isomerization process, but isomerization causes a decrease in the fluorescence quantum yield of the dye.
Biconformal Supergravity And A Quantum Theory Of Biconformal Space
Anderson, L B
2004-01-01
Biconformal supergravity models provide a new gauging of the superconformal group relevant to the Maldacena conjecture. Using the group quotient method to biconformally gauge SU(2, 2|N ), we generate an (8+8N)-dim superspace. We write the most general even and odd parity actions linear in the curvatures, the bosonic sector of which is known to descend to general relativity on a 4- dim manifold. Further, we claim in addition to being a natural arena for gravity, biconformal space contains the essential elements of quantization. Using three postulates characterizing motion and measurement in biconformal geometry, we derive standard quantum mechanics, and show how the need for probability amplitudes arises from the use of a standard of measurement. Our results include Feynman path integrals, the Schro&huml;dinger equation, the Heisenberg uncertainty relation and fundamental canonical commutation relations. Additionally, we show that a postulate for unique, classical motion yields Hamiltonian dynamics with no...
Energy Technology Data Exchange (ETDEWEB)
Koerting, V., E-mail: koerting@nbi.d [Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel (Switzerland); Niels Bohr Institute, Universitetsparken, DK-2100 Copenhagen (Denmark); The Niels Bohr International Academy, The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Fritsch, P. [Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universitaet, Theresienstrasse 37, 80333 Munich (Germany); Kehrein, S., E-mail: stefan.kehrein@physik.lmu.d [Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universitaet, Theresienstrasse 37, 80333 Munich (Germany)
2011-05-15
Since the experimental realization of Kondo physics in quantum dots, its far-from-equilibrium properties have generated considerable theoretical interest. This is due to the interesting interplay of non-equilibrium physics and correlation effects in this model, which has now been analyzed using several new theoretical methods that generalize renormalization techniques to non-equilibrium situations. While very good agreement between these methods has been found for the spin-1/2 Kondo model, it is desirable to have a better understanding of their applicability for more complicated impurity models. In this paper the differences and commons between two such approaches, namely the flow equation method out of equilibrium and the frequency-dependent poor man's scaling approach are presented for the non-equilibrium double quantum dot system. This will turn out to be a particularly suitable testing ground while being experimentally interesting in its own right. An outlook is given on the quantum critical behavior of the double quantum dot system and its accessibility with the two methods.
Filippone, Michele; Mora, Christophe
2012-01-01
We formulate a general approach for studying the low-frequency response of an interacting quantum dot connected to leads in the presence of oscillating gate voltages. The energy dissipated is characterized by the charge relaxation resistance, which under the loose assumption of Fermi liquid behavior at low energy, is shown to depend only on static charge susceptibilities. The predictions of the scattering theory are recovered in the noninteracting limit while the effect of interactions is sim...
Holography, Quantum Geometry, and Quantum Information Theory
Directory of Open Access Journals (Sweden)
P. A. Zizzi
2000-03-01
Full Text Available Abstract: We interpret the Holographic Conjecture in terms of quantum bits (qubits. N-qubit states are associated with surfaces that are punctured in N points by spin networks' edges labelled by the spin-Ã‚Â½ representation of SU(2, which are in a superposed quantum state of spin "up" and spin "down". The formalism is applied in particular to de Sitter horizons, and leads to a picture of the early inflationary universe in terms of quantum computation. A discrete micro-causality emerges, where the time parameter is being defined by the discrete increase of entropy. Then, the model is analysed in the framework of the theory of presheaves (varying sets on a causal set and we get a quantum history. A (bosonic Fock space of the whole history is considered. The Fock space wavefunction, which resembles a Bose-Einstein condensate, undergoes decoherence at the end of inflation. This fact seems to be responsible for the rather low entropy of our universe.
On the composition of an arbitrary collection of SU(2) spins: an enumerative combinatoric approach
Gyamfi, J. A.; Barone, V.
2018-03-01
The whole enterprise of spin compositions can be recast as simple enumerative combinatoric problems. We show here that enumerative combinatorics (Stanley 2011 Enumerative Combinatorics (Cambridge Studies in Advanced Mathematics vol 1) (Cambridge: Cambridge University Press)) is a natural setting for spin composition, and easily leads to very general analytic formulae—many of which hitherto not present in the literature. Based on it, we propose three general methods for computing spin multiplicities; namely, (1) the multi-restricted composition, (2) the generalized binomial and (3) the generating function methods. Symmetric and anti-symmetric compositions of SU(2) spins are also discussed, using generating functions. Of particular importance is the observation that while the common Clebsch–Gordan decomposition—which considers the spins as distinguishable—is related to integer compositions, the symmetric and anti-symmetric compositions (where one considers the spins as indistinguishable) are obtained considering integer partitions. The integers in question here are none other than the occupation numbers of the Holstein–Primakoff bosons. The pervasiveness of q-analogues in our approach is a testament to the fundamental role they play in spin compositions. In the appendix, some new results in the power series representation of Gaussian polynomials (or q-binomial coefficients)—relevant to symmetric and antisymmetric compositions—are presented.
Non-Local effective SU(2) Polyakov-loop models from inverse Monte-Carlo methods
Bahrampour, Bardiya; von Smekal, Lorenz
2016-01-01
The strong-coupling expansion of the lattice gauge action leads to Polyakov-loop models that effectively describe gluodynamics at low temperatures, and together with the hopping expansion of the fermion determinant provides insight into the QCD phase diagram at finite density and low temperatures, although for rather heavy quarks. At higher temperatures the strong-coupling expansion breaks down and it is expected that the interactions between Polyakov loops become non-local. Here, we therefore test how well pure SU(2) gluodynamics can be mapped onto different non-local Polyakov models with inverse Monte-Carlo methods. We take into account Polyakov loops in higher representations and gradually add interaction terms at larger distances. We are particularly interested in extrapolating the range of non-local terms in sufficiently large volumes and higher representations. We study the characteristic fall-off in strength of the non-local couplings with the interaction distance, and its dependence on the gauge coupl...
A nonlinear deformed su(2) algebra with a two-colour quasitriangular Hopf structure
Bonatsos, Dennis; Kolokotronis, P; Ludu, A; Quesne, C
1996-01-01
Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J_0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some of them with a Hopf algebraic structure is addressed by studying in detail a specific example, referred to as ${\\cal A}^+_q(1)$. This algebra is shown to possess two series of (N+1)-dimensional unitary irreducible representations, where N=0, 1, 2, .... To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed by proceeding in two steps. In the first one, a variant and extension of the deforming functional technique is introduced: variant because a map between two deformed algebras, su_q(2) and ${\\cal A}^+_q(1)$, is considered instead of a map between a Lie algebra and a deformed one, and extension because use is made of a two-valued functional, whose inverse is singular. As a result, the Hopf structure of su_q(2) is car...
SU(2) Gauge Theory with Two Fundamental Flavours: a Minimal Template for Model Building
Arthur, Rudy; Hansen, Martin; Hietanen, Ari; Pica, Claudio; Sannino, Francesco
2016-01-01
We investigate the continuum spectrum of the SU(2) gauge theory with $N_f=2$ flavours of fermions in the fundamental representation. This model provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics that range from composite (Goldstone) Higgs theories to several intriguing types of dark matter candidates, such as the SIMPs. We improve our previous lattice analysis [1] by adding more data at light quark masses, at two additional lattice spacings, by determining the lattice cutoff via a Wilson flow measure of the $w_0$ parameter, and by measuring the relevant renormalisation constants non-perturbatively in the RI'-MOM scheme. Our results for the lightest isovector states in the vector and axial channels, in units of the pseudoscalar decay constant, are $m_V/F_{\\rm{PS}}\\sim 13.1(2.2)$ and $m_A/F_{\\rm{PS}}\\sim 14.5(3.6)$ (combining statistical and systematic errors). In the context of the composite (Goldstone) Higgs models, our result for the spin-...
CKM and PMNS Mixing Matrices from Discrete Subgroups of SU(2
Directory of Open Access Journals (Sweden)
Potter F.
2014-07-01
Full Text Available One of the greatest challenges in particle physics is to determine the first principles origin of the quark and lepton mixing matrices CKM and PMNS that relate the flavor states to the mass states. This first principles derivation of both the PMNS and CKM matrices utilizes quaternion generators of the three discrete (i.e., finite binary rotational subgroups of SU(2 called [3,3,2], [4,3,2], and [5,3,2] for three lepton families in R 3 and four related discrete binary rotational subgroups [3,3,3], [4,3,3], [3,4,3], and [5,3,3] represented by four quark families in R 4 . The traditional 3 3 CKM matrix is extracted as a submatrix of the 4 4 CKM4 matrix. The predicted fourth family of quarks has not been discovered yet. If these two additional quarks exist, there is the possibility that the Standard Model lagrangian may apply all the way down to the Planck scale.
Ladd, T D; Jelezko, F; Laflamme, R; Nakamura, Y; Monroe, C; O'Brien, J L
2010-03-04
Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future.
The Infrared behaviour of the gluon propagator in SU(2) and SU(3) without lattice Gribov copies
Alexandrou, C; Follana, E; De Forcrand, Ph
2000-01-01
We present lattice results for the gluon propagator for SU(2) and SU(3) in the Laplacian gauge which avoids lattice Gribov copies. In SU(3) we compare with the most recent lattice calculation in Landau gauge and with various approximate solutions of the Dyson Schwinger equations (DSE).
Ksenofontov, M. A.; Bobkova, E. Yu.; Shundalau, M. B.; Ostrovskaya, L. E.; Vasil'eva, V. S.
2017-11-01
The interaction of the functional groups in the polyurethane foam adsorbent Penopurm® with the cations of some 3d-metals upon their extraction from aqueous solutions has been studied by atomic emission spectroscopy, UV/Vis and vibrational IR spectroscopy, and quantum chemical simulation using density functional theory. Penopurm® absorbs 3d-metal cations from aqueous solutions in the pH range 5-7. Some spectral criteria have been found indicating a predominant interaction of Ni2+ ions with various fragments of the polyurethane foam structure.
Zhang, Run-wu; Ji, Wei-xiao; Zhang, Chang-wen; Li, Ping; Wang, Pei-ji
2016-01-01
Quantum spin Hall (QSH) effect is promising for achieving dissipationless transport devices due to the robust gapless states inside insulating bulk gap. Here, by using first-principles calculations, we discover group-IV chalcogenide Si2Te2 film to be a 2D QSH insulator with a fundamental band gap of 0.29 eV, which is tunable under external strain. This nontrivial topological phase stems from band inversion between the Si-px,y and Te-px,y orbitals, demonstrated by a single pair of topologicall...
Lattice simulation of a center symmetric three dimensional effective theory for SU(2) Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Smith, Dominik
2010-11-17
We present lattice simulations of a center symmetric dimensionally reduced effective field theory for SU(2) Yang Mills which employ thermal Wilson lines and three-dimensional magnetic fields as fundamental degrees of freedom. The action is composed of a gauge invariant kinetic term, spatial gauge fields and a potential for theWilson line which includes a ''fuzzy'' bag term to generate non-perturbative fluctuations between Z(2) degenerate ground states. The model is studied in the limit where the gauge fields are set to zero as well as the full model with gauge fields. We confirm that, at moderately weak coupling, the ''fuzzy'' bag term leads to eigenvalue repulsion in a finite region above the deconfining phase transition which shrinks in the extreme weak-coupling limit. A non-trivial Z(N) symmetric vacuum arises in the confined phase. The effective potential for the Polyakov loop in the theory with gauge fields is extracted from the simulations including all modes of the loop as well as for cooled configurations where the hard modes have been averaged out. The former is found to exhibit a non-analytic contribution while the latter can be described by a mean-field like ansatz with quadratic and quartic terms, plus a Vandermonde potential which depends upon the location within the phase diagram. Other results include the exact location of the phase boundary in the plane spanned by the coupling parameters, correlation lengths of several operators in the magnetic and electric sectors and the spatial string tension. We also present results from simulations of the full 4D Yang-Mills theory and attempt to make a qualitative comparison to the 3D effective theory. (orig.)
Padilha, J E; Pontes, R B; Schmidt, T M; Miwa, R H; Fazzio, A
2016-05-23
We predict a new class of large band gap quantum spin Hall insulators, the fluorinated PbX (X = C, Si, Ge and Sn) compounds, that are mechanically stable two-dimensional materials. Based on first principles calculations we find that, while the PbX systems are not topological insulators, all fluorinated PbX (PbXF2) compounds are 2D topological insulators. The quantum spin Hall insulating phase was confirmed by the explicitly calculation of the Z2 invariant. In addition we performed a thorough investigation of the role played by the (i) fluorine saturation, (ii) crystal field, and (iii) spin-orbital coupling in PbXF2. By considering nanoribbon structures, we verify the appearance of a pair of topologically protected Dirac-like edge states connecting the conduction and valence bands. The insulating phase which is a result of the spin orbit interaction, reveals that this new class of two dimensional materials present exceptional nontrivial band gaps, reaching values up to 0.99 eV at the Γ point, and an indirect band gap of 0.77 eV. The topological phase is arisen without any external field, making this system promising for nanoscale applications, using topological properties.
Finite and profinite quantum systems
Vourdas, Apostolos
2017-01-01
This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics. The first major part of this monograph studies the so-called `qubits' and `qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied. The second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers. Applications of the formalism include quantum optics and ...
Jang, Min-Ho; Yang, Hyunseung; Chang, Yun Hee; Park, Hyun-Chul; Park, Hyeonjung; Cho, Han Hee; Kim, Bumjoon J; Kim, Yong-Hyun; Cho, Yong-Hoon
2017-10-13
Oxygen-containing functional groups such as epoxy, hydroxyl, carboxylic, and carboxyl groups have a great influence on the luminescence properties of graphene oxide quantum dots (GOQDs). Understanding their roles is essential for the design and optimization of GOQD performance. Herein, we investigate the effect of epoxide functional groups in GOQDs on the luminescence mechanism through passivation of the epoxide functional groups using the alkyl ligand oleylamine. Luminescence in the as-synthesized GOQDs has two separate origins: intrinsic states derived from localized sp(2) carbon subdomains and extrinsic states formed by oxygen-functional groups. When the oleylamine ligand is conjugated on the GOQDs, intrinsic PL emission from the localized sp(2) carbon subdomains decreases. This is discussed in detail, based on optical characterization and first-principles density functional theory calculations, which reveal that the role of the epoxide functional groups is to form localized sp(2) carbon subdomains emitting intrinsic PL. To the best of our knowledge, this is the first investigation of the role of epoxide functional groups on the luminescence mechanism in GOQDs.
Quantum Erasure: Quantum Interference Revisited
Walborn, Stephen P.; Cunha, Marcelo O. Terra; Pádua, Sebastião; Monken, Carlos H.
2005-01-01
Recent experiments in quantum optics have shed light on the foundations of quantum physics. Quantum erasers - modified quantum interference experiments - show that quantum entanglement is responsible for the complementarity principle.
Instantons, vortices and confinement in SU(2) Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Lemos, A.L.L. de [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil); Oxman, L.E.; Teixeira, B.F.I. [Universidade Federal Fluminense (UFF), Niteroi, RJ (Brazil)
2012-07-01
Full text: In this work, we derive a recently proposed Abelian model to describe the interaction of correlated instantons, center vortices, and dual fields in three dimensional SU(2) Yang-Mills theory. Correlated monopoles and center vortices are believed to play a relevant role in accommodating the different properties of the confining string in Yang-Mills theories, receiving support from lattice simulations. In fact, scenarios based on either monopoles or closed center vortices are only partially successful to describe the expected behavior of the potential between quarks. At asymptotic distances, this potential should be linear and depend on the representation of the subgroup Z(N) of SU(N) (N-ality). At intermediate scales, it should posses Casimir scaling. The Cho-Faddeev- Niemi representation (CFN) can be used to associate monopoles with defects of the local color frame used to decompose the gauge fields. This possible frame defects can be extended to describe not only monopoles but also center vortices, correlated or not. In these scenarios, one of the difficulties is how to deal with the integration over an ensemble of extended objects, after considering a phenomenological parametrization of their properties, such as stiffness, interactions with dual fields, and interactions between them. This is particularly severe in four dimensional theories where center vortices generate two dimensional extended world surfaces. However, in three dimensions center vortices are stringlike and an ensemble of world lines is naturally associated with a second quantized field theory. The aim of this work is presenting a careful derivation of an effective model, considering instantons and center vortices in D=3 SU(3) theory, after parameterizing some intrinsic physical properties that these objects could present. One of the fundamental ingredients will be the adoption of recent techniques borrowed from polymer physics, where the extended objects are also one dimensional. This
Simplicial gauge theory and quantum gauge theory simulation
Energy Technology Data Exchange (ETDEWEB)
Halvorsen, Tore Gunnar, E-mail: toregha@gmail.com [Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim (Norway); Sorensen, Torquil Macdonald, E-mail: t.m.sorensen@matnat.uio.no [Centre of Mathematics for Applications, University of Oslo, NO-0316 Oslo (Norway)
2012-01-01
We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed for several SU(2) gauge fields. Additionally, we perform simplicial Monte Carlo quantum gauge field simulations involving measurements of the action as well as differently sized Wilson loops as functions of {beta}.
Stumpf, H.
2003-01-01
Generalized de Broglie-Bargmann-Wigner (BBW) equations are relativistically invariant quantum mechanical many body equations with nontrivial interaction, selfregularization and probability interpretation. Owing to these properties these equations are a suitable means for describing relativistic bound states of fermions. In accordance with de Broglie's fusion theory and modern assumptions about the partonic substructure of elementary fermions, i.e., leptons and quarks, the three-body generalized BBW-equations are investigated. The transformation properties and quantum numbers of the three-parton equations under the relevant group actions are elaborated in detail. Section 3 deals with the action of the isospin group SU(2), a U(1) global gauge group for the fermion number, the hypercharge and charge generators. The resulting quantum numbers of the composite partonic systems can be adapted to those of the phenomenological particles to be described. The space-time transformations and in particular rotations generated by angular momentum operators are considered in Section 4. Based on the compatibility of the BBW-equations and the group theoretical constraints, in Sect. 5 integral equations are formulated in a representation with diagonal energy and total angular momentum variables. The paper provides new insight into the solution space and quantum labels of resulting integral equations for three parton states and prepares the ground for representing leptons and quarks as composite systems.
Deconfined quantum critical points: symmetries and dualities
Wang, Chong; Nahum, Adam; Metlitski, Max; Xu, Cenke; Senthil, T.
The deconfined quantum critical point (QCP) between the Neel and the valence bond solid (VBS) phases was proposed as an example of (2 + 1) d conformal field theories that are fundamentally different from all the standard Landau-Ginzburg-Wilson-Fisher fixed points. In this work we demonstrate that the deconfined QCP, both the easy-plane version and the version with an explicit SU(2) spin symmetry, have multiple equivalent descriptions. In particular, the easy-plane deconfined QCP, besides its self-duality that was discussed before, is also dual to the Nf = 2 fermionic quantum electrodynamics (QED), which has its own self-duality and hence has an O(4) ×Z2T symmetry; the deconfined QCP with the explicit SU(2) spin symmetry is dual to the Nf = 2 QED-Gross-Neveu fixed point, and could have an emergent SO(5) symmetry, as was conjectured before.
Indian Academy of Sciences (India)
groups and their representation theory. The notions of quantum subgroups and quan- tum homogeneous spaces were soon introduced by Podles [15]. The most well-known example of compact quantum group is the q-deformation of the SU(n) group whose representation theory was obtained by Vaksman and Soibelman ...
Topics in string theory and quantum gravity
Alvarez-Gaume, Luis
1992-01-01
These are the lecture notes for the Les Houches Summer School on Quantum Gravity held in July 1992. The notes present some general critical assessment of other (non-string) approaches to quantum gravity, and a selected set of topics concerning what we have learned so far about the subject from string theory. Since these lectures are long (133 A4 pages), we include in this abstract the table of contents, which should help the user of the bulletin board in deciding whether to latex and print the full file. 1-FIELD THEORETICAL APPROACH TO QUANTUM GRAVITY: Linearized gravity; Supergravity; Kaluza-Klein theories; Quantum field theory and classical gravity; Euclidean approach to Quantum Gravity; Canonical quantization of gravity; Gravitational Instantons. 2-CONSISTENCY CONDITIONS: ANOMALIES: Generalities about anomalies; Spinors in 2n dimensions; When can we expect to find anomalies?; The Atiyah-Singer Index Theorem and the computation of anomalies; Examples: Green-Schwarz cancellation mechanism and Witten's SU(2) ...
Thermoelectric transport through quantum dots
Energy Technology Data Exchange (ETDEWEB)
Merker, Lukas Heinrich
2016-06-30
In this thesis the thermoelectric properties (electrical conductance, Seebeck coefficient and thermal conductance)of quantum dots described by the Anderson impurity model have been investigated by using the numerical renormalization group (NRG) method. In order to make accurate calculations for thermoelectric properties of quantum impurity systems, a number of recent developments and refinements of the NRG have been implemented. These include the z-averaging and Campo discretization scheme, which enable the evaluation of physical quantities on an arbitrary temperature grid and at large discretization parameter Λ and the full density matrix (FDM) approach, which allows a more accurate calculation of spectral functions and transport coefficients. The implementation of the z-averaging and Campo discretization scheme has been tested within a new method for specific heats of quantum impurities. The accuracy of this new method was established by comparison with the numerical solution of the Bethe-ansatz equations for the Anderson model. The FDM approach was implemented and tested within a new approach to the calculation of impurity contributions to the uniform susceptibilities. Within this method a non-negligible contribution from the ''environmental'' degrees of freedom needs to be taken into account to recover the correct susceptibility, as shown by comparison with the Bethe-ansatz approach. An accurate method to calculate the conductance of a quantum dot is implemented, enabling the extraction of the Fermi liquid scaling coefficients c{sub T} and c{sub B} to high accuracy, being able to verify the results of the renormalized super perturbation theory approach (within its regime of validity). The method was generalized to higher order moments of the local level spectral function. This, as well as reduction of the SU(2) code to the U(1) symmetry, enabled the investigation of the effect of a magnetic field on the thermoelectric properties of quantum
Li, Shu-shen; Long, Gui-Lu; Bai, Feng-Shan; Feng, Song-Lin; Zheng, Hou-Zhi
2001-01-01
Quantum computing is a quickly growing research field. This article introduces the basic concepts of quantum computing, recent developments in quantum searching, and decoherence in a possible quantum dot realization.
Symmetries and groups in particle physics; Symmetrien und Gruppen in der Teilchenphysik
Energy Technology Data Exchange (ETDEWEB)
Scherer, Stefan [Mainz Univ. (Germany)
2016-07-01
The aim of this book consists of a didactic introduction to the group-theoretical considerations and methods, which have led to an ever deeper understanding of the interactions of the elementary particles. The first three chapters deal primarily with the foundations of the representation theory of primarily finite groups, whereby many results are also transferable to compact Lie groups. In the third chapter we discuss the concept of Lie groups and their connection with Lie algebras. In the remaining chapter it is mainly about the application of group theory in physics. Chapter 4 deals with the groups SO(3) and SU(2), which occur in connection with the description of the angular momentum in quantum mechanics. We discuss the Wigner-Eckar theorem together with some applications. In chapter 5 we are employed to the composition properties of strongly interacting systems, so called hadrons, and discuss extensively the transformation properties of quarks with relation to the special unitary groups. The Noether theorem is generally treated in connection to the conservation laws belonging to the Galilei group and the Poincare group. We confine us in chapter 6 to internal symmetries, but explain for that extensively the application to quantum field theory. Especially an outlook on the effect of symmetries in form of so called Ward identities is granted. In chapter 7 we turn towards the gauge principle and discuss first the construction of quantum electrodynamics. In the following we generalize the gauge principle to non-Abelian groups (Yang-Mills theories) and formulate the quantum chromodynamics (QCD). Especially we take a view of ''random'' global symmetries of QCD, especially the chiral symmetry. In chapter 8 we illuminate the phenomenon of spontaneous symmetry breaking both for global and for local symmetries. In the final chapter we work out the group-theoretical structure of the Standard Model. Finally by means of the group SU(5) we take a view to
Quantum independent increment processes
Franz, Uwe
2006-01-01
This is the second of two volumes containing the revised and completed notes of lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald in March, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present second volume contains the following lectures: "Random Walks on Finite Quantum Groups" by Uwe Franz and Rolf Gohm, "Quantum Markov Processes and Applications in Physics" by Burkhard Kümmerer, Classical and Free Infinite Divisibility and Lévy Processes" by Ole E. Barndorff-Nielsen, Steen Thorbjornsen, and "Lévy Processes on Quantum Groups and Dual Groups" by Uwe Franz.
Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid
Energy Technology Data Exchange (ETDEWEB)
Calzada, J A [Departamento de Matematica Aplicada, Escuela Superior de Ingenieros Industriales, Universidad de Valladolid, 47011 Valladolid (Spain); Kuru, S [Department of Physics, Faculty of Science, Ankara University, 06100 Ankara (Turkey); Negro, J; Olmo, M A del [Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid (Spain)], E-mail: juacal@eis.uva.es, E-mail: kuru@science.ankara.edu.tr, E-mail: jnegro@fta.uva.es, E-mail: olmo@fta.uva.es
2008-06-27
A class of quantum superintegrable Hamiltonians defined on a two-dimensional hyperboloid is considered together with a set of intertwining operators connecting them. It is shown that such intertwining operators close a su(2, 1) Lie algebra and determine the Hamiltonians through the Casimir operators. By means of discrete symmetries a broader set of operators is obtained closing a so(4, 2) algebra. The physical states corresponding to the discrete spectrum of bound states as well as the degeneration are characterized in terms of unitary representations of su(2, 1) and so(4, 2)
Quantum Fluctuations along Symmetry Crossover in a Kondo-Correlated Quantum Dot
Ferrier, Meydi; Arakawa, Tomonori; Hata, Tokuro; Fujiwara, Ryo; Delagrange, Raphaëlle; Deblock, Richard; Teratani, Yoshimichi; Sakano, Rui; Oguri, Akira; Kobayashi, Kensuke
2017-05-01
Universal properties of entangled many-body states are controlled by their symmetry and quantum fluctuations. By the magnetic-field tuning of the spin-orbital degeneracy in a Kondo-correlated quantum dot, we have modified quantum fluctuations to directly measure their influence on the many-body properties along the crossover from SU(4) to SU(2) symmetry of the ground state. High-sensitive current noise measurements combined with the nonequilibrium Fermi liquid theory clarify that the Kondo resonance and electron correlations are enhanced as the fluctuations, measured by the Wilson ratio, increase along the symmetry crossover. Our achievement demonstrates that nonlinear noise constitutes a measure of quantum fluctuations that can be used to tackle quantum phase transitions.
Theory of long-lived nuclear spin states in methyl groups and quantum-rotor induced polarisation.
Dumez, Jean-Nicolas; Håkansson, Pär; Mamone, Salvatore; Meier, Benno; Stevanato, Gabriele; Hill-Cousins, Joseph T; Roy, Soumya Singha; Brown, Richard C D; Pileio, Giuseppe; Levitt, Malcolm H
2015-01-28
Long-lived nuclear spin states have a relaxation time much longer than the longitudinal relaxation time T1. Long-lived states extend significantly the time scales that may be probed with magnetic resonance, with possible applications to transport and binding studies, and to hyperpolarised imaging. Rapidly rotating methyl groups in solution may support a long-lived state, consisting of a population imbalance between states of different spin exchange symmetries. Here, we expand the formalism for describing the behaviour of long-lived nuclear spin states in methyl groups, with special attention to the hyperpolarisation effects observed in (13)CH3 groups upon rapidly converting a material with low-barrier methyl rotation from the cryogenic solid state to a room-temperature solution [M. Icker and S. Berger, J. Magn. Reson. 219, 1 (2012)]. We analyse the relaxation properties of methyl long-lived states using semi-classical relaxation theory. Numerical simulations are supplemented with a spherical-tensor analysis, which captures the essential properties of methyl long-lived states.
SiNx-induced intermixing in AlInGaAs/InP quantum well through interdiffusion of group III atoms
Lee, Ko-Hsin; Thomas, Kevin; Gocalińska, Agnieszka M.; Manganaro, Marina; Pelucchi, Emanuele; Peters, Frank H.; Corbett, Brian M.
2012-01-01
We analyze the composition profiles within intermixed and non-intermixed AlInGaAs-based multiple quantum wells structures by secondary ion mass spectrometry and observe that the band gap blue shift is mainly attributed to the interdiffusion of In and Ga atoms between the quantum wells and the barriers. Based on these results, several AlInGaAs-based single quantum well (SQW) structures with various compressive strain (CS) levels were grown and their photoluminescence spectra were investigated ...
Quantum Distinction: Quantum Distinctiones!
Zeps, Dainis
2009-01-01
10 pages; How many distinctions, in Latin, quantum distinctiones. We suggest approach of anthropic principle based on anthropic reference system which should be applied equally both in theoretical physics and in mathematics. We come to principle that within reference system of life subject of mathematics (that of thinking) should be equated with subject of physics (that of nature). For this reason we enter notions of series of distinctions, quantum distinction, and argue that quantum distinct...
Spin-k/2-spin-k/2 SU(2) two-point functions on the torus
Energy Technology Data Exchange (ETDEWEB)
Kirsch, Ingo [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie; Kucharski, Piotr [Warsaw Univ. (Poland). Inst. of Theoretical Physics
2012-11-15
We discuss a class of two-point functions on the torus of primary operators in the SU(2) Wess-Zumino-Witten model at integer level k. In particular, we construct an explicit expression for the current blocks of the spin-(k)/(2)-spin-(k)/(2) torus two-point functions for all k. We first examine the factorization limits of the proposed current blocks and test their monodromy properties. We then prove that the current blocks solve the corresponding Knizhnik-Zamolodchikov-like differential equations using the method of Mathur, Mukhi and Sen.
SU(2 color NJL model and EOS of quark-hadron matter at finite temperature and density
Directory of Open Access Journals (Sweden)
Weise Wolfram
2012-02-01
Full Text Available We study the NJL model with the Polyakov loop in the SU(2-color case for the EOS of quark-hadron matter at finite temperature and density. We consider the spontaneous chiral symmetry breaking and the diquark condensation together with the behavior of the Polyakov loop for the phase diagram of quark-hadron matter. We discuss the spectrum of mesons and diquark baryons (boson at finite temperature and density.We derive also the linear sigma model Lagrangian for diquark baryon and mesons.
A note on open-chain transfer matrices from q-deformed su(2 vertical stroke 2)S-matrices
Energy Technology Data Exchange (ETDEWEB)
Murgan, R. [Physics Department, Gustavus Adolphus College, St. Peter, MN (United States)
2009-09-15
In this note, we perform Sklyanin's construction of commuting open-chain/boundary transfer matrices to the q-deformed SU(2 vertical stroke 2) bulk S-matrix of Beisert and Koroteev and a corresponding boundary S-matrix. This also includes a corresponding commuting transfer matrix using the graded version of the q-deformed bulk S-matrix. Utilizing the crossing property for the bulk S-matrix, we argue that the transfer matrix for both graded and non-graded versions contains a crucial factor which is essential for commutativity. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
Magneto-dimensional resonance. Pseudospin phase and hidden quantum number
Karasev, M. V.
2017-07-01
The Schrödinger operator for a spinless charge inside a layer with parabolic confinement profile and homogeneous magnetic field is considered. The Lorentz (cyclotron) and the confinement frequencies are assumed to be equal to each other. After inclination of the layer normal from the magnetic field direction there appears a pseudospin su(2)-field removing the resonance degeneracy of Landau levels. Under deviations of the layer surface from the plane shape, a longitudinal geometric current is created. In circulations around surface warping, there is a nontrivial quantum phase transition generated by an element of the π1-homotopy group and a hidden degree of freedom (spectral degeneracy) associated with a "charge" of geometric poles on the layer. The quantization rule contains an additional parity index related to the algebraic number of geometric poles and the Landau level number. The resonance pseudospin phase-shift represents an example of general Aharonov-Bohm type topologic phenomena in quantum (semiclassical or adiabatic) systems with delta-function singularities in symplectic structure.
Higher representations on the lattice: numerical simulations. SU(2) with adjoint fermions
DEFF Research Database (Denmark)
Del Debbio, Luigi; Patella, Agostino; Pica, Claudio
2008-01-01
We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present in detail the implementation of the HMC/RHMC algorithm for simulating dynamical fermions. We discuss the validation of the implementation through an extensive set of tes...
Ibort, A.; López Yela, A.; Moro, J.
2017-10-01
A numerical algorithm that computes the decomposition of any finite-dimensional unitary reducible representation of a compact Lie group is presented. The algorithm, which does not rely on an algebraic insight into the group structure, is inspired by quantum mechanical notions. After generating two adapted states (these objects will be conveniently defined in Definition II.1) and after appropriate algebraic manipulations, the algorithm returns the block matrix structure of the representation in terms of its irreducible components. It also provides an adapted orthonormal basis. The algorithm can be used to compute the Clebsch-Gordan coefficients of the tensor product of irreducible representations of a given compact Lie group. The performance of the algorithm is tested on various examples: the decomposition of the regular representation of two finite groups and the computation of Clebsch-Gordan coefficients of two examples of tensor products of representations of SU(2).
Quantum cluster algebra structures on quantum nilpotent algebras
Goodearl, K R
2017-01-01
All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts.
Energy Technology Data Exchange (ETDEWEB)
Sarma, Runjun; Mohanta, Dambarudhar, E-mail: best@tezu.ernet.in
2017-02-01
We report on the radiative emission decay dynamics of a less known, γ-phase manganese selenide quantum dot system (MnSe QDs) subjected to bio-functionalization. A short-ligand thioglycolic acid (TGA), and a long-chain sodium dodecyl sulfate (SDS) surfactants were used as surface anchors prior bioconjugation with albumin proteins (BSA). Time resolved photoluminescence (TR-PL) spectra of the QDs have revealed bi-exponential decay trends with the fast (τ{sub 1}) and slow (τ{sub 2}) decay parameters assigned to the core state recombination and surface trapped excitons; respectively. The average lifetime (τ{sub avg}) was found to get shortened from a value of ∼0.87 ns–0.72 ns in unconjugated and BSA conjugated MnSe-TGA QDs; respectively. Conversely, MnSe-SDS QDs with BSA conjugation exhibited nearly four-fold enhancement of τ{sub avg} with respect to its unconjugated counterpart. Moreover, a considerable amount of Förster resonance energy transfer (FRET) was found to occur from the TGA coated MnSe QDs to BSA and with an ensuing efficiency of ∼61%. The origin of anomalous carrier life-time relaxation features has also been encountered through a simplified model as regards head group interaction experienced by the MnSe QDs with different surfactant types. Exploiting luminescence decay characteristics of a magneto-fluorescent candidate could find immense scope in diverse biological applications including assays, labeling and imaging. - Highlights: • Surface anchored manganese selenide quantum dots (MnSe QDs) have been synthesized via a physico-chemical reduction route. • Time resolved luminescence spectra of the QDs have displayed bi-exponential decay trend. • Thioglycolic acid (TGA) coated QDs exhibited shorter lifetime as compared to sodium dodecyl sulfo-succinate (SDS) coated ones. • Upon BSA conjugation, the average life time is four-fold enhanced in MnSe-SDS QDs. • An efficient FRET process has been revealed in BSA conjugated TGA coated MnSe QDs.
Baaquie, Belal E; Demongeot, J; Galli-Carminati, Giuliana; Martin, F; Teodorani, Massimo
2015-01-01
At the end of the 19th century Sigmund Freud discovered that our acts and choices are not only decisions of our consciousness, but that they are also deeply determined by our unconscious (the so-called "Freudian unconscious"). During a long correspondence between them (1932-1958) Wolfgang Pauli and Carl Gustav Jung speculated that the unconscious could be a quantum system. This book is addressed both to all those interested in the new developments of the age-old enquiry in the relations between mind and matter, and also to the experts in quantum physics that are interested in a formalisation of this new approach. The description of the "Bilbao experiment" adds a very interesting experimental inquiry into the synchronicity effect in a group situation, linking theory to a quantifiable verification of these subtle effects. Cover design: "Entangled Minds". Riccardo Carminati Galli, 2014.
Quantum Nanostructures by Droplet Epitaxy
Directory of Open Access Journals (Sweden)
Somsak Panyakeow
2009-02-01
Full Text Available Droplet epitaxy is an alternative growth technique for several quantum nanostructures. Indium droplets are distributed randomly on GaAs substrates at low temperatures (120-350'C. Under background pressure of group V elements, Arsenic and Phosphorous, InAs and InP nanostructures are created. Quantum rings with isotropic shape are obtained at low temperature range. When the growth thickness is increased, quantum rings are transformed to quantum dot rings. At high temperature range, anisotropic strain gives rise to quantum rings with square holes and non-uniform ring stripe. Regrowth of quantum dots on these anisotropic quantum rings, Quadra-Quantum Dots (QQDs could be realized. Potential applications of these quantum nanostructures are also discussed.
Geometrization of Quantum Mechanics
Carinena, J. F.; Clemente-Gallardo, J.; Marmo, G.
2007-01-01
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.
Symmetry-protected quantum spin Hall phases in two dimensions.
Liu, Zheng-Xin; Wen, Xiao-Gang
2013-02-08
Symmetry-protected topological (SPT) states are short-range entangled states with symmetry. Nontrivial SPT states have symmetry-protected gapless edge excitations. In 2 dimension (2D), there are an infinite number of nontrivial SPT phases with SU(2) or SO(3) symmetry. These phases can be described by SU(2) or SO(3) nonlinear-sigma models with a quantized topological θ term. At an open boundary, the θ term becomes the Wess-Zumino-Witten term and consequently the boundary excitations are decoupled gapless left movers and right movers. Only the left movers (if θ>0) carry the SU(2) or SO(3) quantum numbers. As a result, the SU(2) SPT phases have a half-integer quantized spin Hall conductance and the SO(3) SPT phases have an even-integer quantized spin Hall conductance. Both the SU(2) and SO(3) SPT phases are symmetric under their U(1) subgroup and can be viewed as U(1) SPT phases with even-integer quantized Hall conductance.
Hartle, James B.
2018-01-01
A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the universe's spacetime geometry and matter content. These consequences follow: (a) The universe generally exhibits different quantum multiverses at different levels and kinds of coarse graining. (b) Quantum multiverses are not a choice or an assumption but ar...
Traub, Joseph F.
2014-01-01
The aim of this thesis was to explain what quantum computing is. The information for the thesis was gathered from books, scientific publications, and news articles. The analysis of the information revealed that quantum computing can be broken down to three areas: theories behind quantum computing explaining the structure of a quantum computer, known quantum algorithms, and the actual physical realizations of a quantum computer. The thesis reveals that moving from classical memor...
Domain walls and perturbation theory in high temperature gauge theory SU(2) in 2+1 dimensions
Korthals-Altes, C P; Stephanov, M A; Teper, M; Altes, C Korthals
1997-01-01
We study the detailed properties of Z_2 domain walls in the deconfined high temperature phase of the d=2+1 SU(2) gauge theory. These walls are studied both by computer simulations of the lattice theory and by one-loop perturbative calculations. The latter are carried out both in the continuum and on the lattice. We find that leading order perturbation theory reproduces the detailed properties of these domain walls remarkably accurately even at temperatures where the effective dimensionless expansion parameter, g^2/T, is close to unity. The quantities studied include the surface tension, the action density profiles, roughening and the electric screening mass. It is only for the last quantity that we find an exception to the precocious success of perturbation theory. All this shows that, despite the presence of infrared divergences at higher orders, high-T perturbation theory can be an accurate calculational tool.
Working group report: Quantum chromodynamics
Indian Academy of Sciences (India)
Harish Chandra Research Institute, Allahabad 211 019, India; Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India; Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India; Delhi University, New Delhi 110 019, India; Deutsches Elecktronen Synchrotron DESY, Zeuthen, Germany ...
Tekdaş, Duygu Aydın; Durmuş, Mahmut; Yanık, Hülya; Ahsen, Vefa
Thiol stabilized CdTe quantum dot (QD) nanoparticles were synthesized in aqueous phase and were used as energy donors to tetra-triethyleneoxythia substituted aluminum, gallium and indium phthalocyanines through fluorescence resonance energy transfer (FRET). Energy transfer occurred from the QDs to phthalocyanines upon photoexcitation of the QDs. An enhancement in efficiency of energy transfer with the nature of the carboxylic thiol stabilizer on the QDs was observed. As a result of the nanoparticle and the phthalocyanine mixing, the photoluminescence efficiency of the phthalocyanine moieties in the mixtures does not strictly follow the quantum yields of the bare phthalocyanines. The photochemistry study of phthalocyanines in the presence of the QDs revealed high singlet oxygen quantum yield, hence the possibility of using QDs in combination with phthalocyanines as photosensitizers in photodynamic therapy of cancer. The fluorescence of the CdTe quantum dots-phthalocyanine conjugates (QDs-Pc) were effectively quenched by addition of 1,4-benzoquinone.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Quantum memories: emerging applications and recent advances.
Heshami, Khabat; England, Duncan G; Humphreys, Peter C; Bustard, Philip J; Acosta, Victor M; Nunn, Joshua; Sussman, Benjamin J
2016-11-12
Quantum light-matter interfaces are at the heart of photonic quantum technologies. Quantum memories for photons, where non-classical states of photons are mapped onto stationary matter states and preserved for subsequent retrieval, are technical realizations enabled by exquisite control over interactions between light and matter. The ability of quantum memories to synchronize probabilistic events makes them a key component in quantum repeaters and quantum computation based on linear optics. This critical feature has motivated many groups to dedicate theoretical and experimental research to develop quantum memory devices. In recent years, exciting new applications, and more advanced developments of quantum memories, have proliferated. In this review, we outline some of the emerging applications of quantum memories in optical signal processing, quantum computation and non-linear optics. We review recent experimental and theoretical developments, and their impacts on more advanced photonic quantum technologies based on quantum memories.
Quantum independent increment processes
Franz, Uwe
2005-01-01
This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 – 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present first volume contains the following lectures: "Lévy Processes in Euclidean Spaces and Groups" by David Applebaum, "Locally Compact Quantum Groups" by Johan Kustermans, "Quantum Stochastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.
A quantum kinematics for asymptotically flat spacetimes
Campiglia, Miguel
2014-01-01
We construct a quantum kinematics for asymptotically flat spacetimes based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying Loop Quantum Gravity (LQG) which supports, in addition to the usual LQG operators, the action of `background exponential operators' which are connection dependent operators labelled by `background' $su(2)$ electric fields. KS states have, in addition to the LQG state label corresponding to 1 dimensional excitations of the triad, a label corresponding to a `background' electric field which describes 3 dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields which label the {\\em states} and the background electric fields which label the {\\em operators}. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We...
Lanzagorta, Marco
2011-01-01
This book offers a concise review of quantum radar theory. Our approach is pedagogical, making emphasis on the physics behind the operation of a hypothetical quantum radar. We concentrate our discussion on the two major models proposed to date: interferometric quantum radar and quantum illumination. In addition, this book offers some new results, including an analytical study of quantum interferometry in the X-band radar region with a variety of atmospheric conditions, a derivation of a quantum radar equation, and a discussion of quantum radar jamming.This book assumes the reader is familiar w
Black Hole Entropy from Indistinguishable Quantum Geometric Excitations
Directory of Open Access Journals (Sweden)
Abhishek Majhi
2016-01-01
Full Text Available In loop quantum gravity the quantum geometry of a black hole horizon consists of discrete nonperturbative quantum geometric excitations (or punctures labeled by spins, which are responsible for the quantum area of the horizon. If these punctures are compared to a gas of particles, then the spins associated with the punctures can be viewed as single puncture area levels analogous to single particle energy levels. Consequently, if we assume these punctures to be indistinguishable, the microstate count for the horizon resembles that of Bose-Einstein counting formula for gas of particles. For the Bekenstein-Hawking area law to follow from the entropy calculation in the large area limit, the Barbero-Immirzi parameter (γ approximately takes a constant value. As a by-product, we are able to speculate the state counting formula for the SU(2 quantum Chern-Simons theory coupled to indistinguishable sources in the weak coupling limit.
Ghetmiri, Seyed Amir; Zhou, Yiyin; Margetis, Joe; Al-Kabi, Sattar; Dou, Wei; Mosleh, Aboozar; Du, Wei; Kuchuk, Andrian; Liu, Jifeng; Sun, Greg; Soref, Richard A; Tolle, John; Naseem, Hameed A; Li, Baohua; Mortazavi, Mansour; Yu, Shui-Qing
2017-02-01
A SiGeSn/GeSn/SiGeSn single quantum well structure was grown using an industry standard chemical vapor deposition reactor with low-cost commercially available precursors. The material characterization revealed the precisely controlled material growth process. Temperature-dependent photoluminescence spectra were correlated with band structure calculation for a structure accurately determined by high-resolution x-ray diffraction and transmission electron microscopy. Based on the result, a systematic study of SiGeSn and GeSn bandgap energy separation and barrier heights versus material compositions and strain was conducted, leading to a practical design of a type-I direct bandgap quantum well.
Quantum CPU and Quantum Simulating
Wang, An Min
1999-01-01
Making use of an universal quantum network or QCPU proposed by me [6], some special quantum networks for simulating some quantum systems are given out. Specially, it is obtained that the quantum network for the time evolution operator which can simulate, in general, Schr\\"odinger equation.
Quantum Computer Games: Quantum Minesweeper
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Bojowald, Martin
The universe, ultimately, is to be described by quantum theory. Quantum aspects of all there is, including space and time, may not be significant for many purposes, but are crucial for some. And so a quantum description of cosmology is required for a complete and consistent worldview. At any rate, even if we were not directly interested in regimes where quantum cosmology plays a role, a complete physical description could not stop at a stage before the whole universe is reached. Quantum theory is essential in the microphysics of particles, atoms, molecules, solids, white dwarfs and neutron stars. Why should one expect this ladder of scales to end at a certain size? If regimes are sufficiently violent and energetic, quantum effects are non-negligible even on scales of the whole cosmos; this is realized at least once in the history of the universe: at the big bang where the classical theory of general relativity would make energy densities diverge. 1.Lachieze-Rey, M., Luminet, J.P.: Phys. Rept. 254,135 (1995), gr-qc/9605010 2.BSDeWitt1967Phys. Rev.160511131967PhRv..160.1113D0158.4650410.1103/PhysRev.160.1113DeWitt, B.S.: Phys. Rev. 160(5), 1113 (1967) 3.Wiltshire, D.L.: In: Robson B., Visvanathan N., Woolcock W.S. (eds.) Cosmology: The Physics of the Universe, pp. 473-531. World Scientific, Singapore (1996). gr-qc/0101003 4.Isham C.J.: In: DeWitt, B.S., Stora, R. (eds.) Relativity, Groups and Topology II. Lectures Given at the 1983 Les Houches Summer School on Relativity, Groups and Topology, Elsevier Science Publishing Company (1986) 5.Klauder, J.: Int. J. Mod. Phys. D 12, 1769 (2003), gr-qc/0305067 6.Klauder, J.: Int. J. Geom. Meth. Mod. Phys. 3, 81 (2006), gr-qc/0507113 7.DGiulini1995Phys. Rev. D5110563013381161995PhRvD..51.5630G10.1103/PhysRevD.51.5630Giulini, D.: Phys. Rev. D 51(10), 5630 (1995) 8.Kiefer, C., Zeh, H.D.: Phys. Rev. D 51, 4145 (1995), gr-qc/9402036 9.WFBlythCJIsham1975Phys. Rev. D117684086991975PhRvD..11..768B10.1103/PhysRevD.11.768Blyth, W
Exact partition functions for the Ω-deformed N=2{sup ∗}SU(2) gauge theory
Energy Technology Data Exchange (ETDEWEB)
Beccaria, Matteo; Macorini, Guido [Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento,Via Arnesano, 73100 Lecce (Italy); INFN,Via Arnesano, 73100 Lecce (Italy)
2016-07-12
We study the low energy effective action of the Ω-deformed N=2{sup ∗}SU(2) gauge theory. It depends on the deformation parameters ϵ{sub 1},ϵ{sub 2}, the scalar field expectation value a, and the hypermultiplet mass m. We explore the plane ((m/(ϵ{sub 1})),((ϵ{sub 2})/(ϵ{sub 1}))) looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit ϵ{sub 2}→0. We propose a simple condition on the structure of poles of the k-instanton prepotential and show that it is admissible at a finite set of points in the above plane. At these special points, the prepotential has poles at fixed positions independent on the instanton number. Besides and remarkably, both the instanton partition function and the full prepotential, including the perturbative contribution, may be given in closed form as functions of the scalar expectation value a and the modular parameter q appearing in special combinations of Eisenstein series and Dedekind η function. As a byproduct, the modular anomaly equation can be tested at all orders at these points. We discuss these special features from the point of view of the AGT correspondence and provide explicit toroidal 1-blocks in non-trivial closed form. The full list of solutions with 1, 2, 3, and 4 poles is determined and described in details.
Width and string tension of the flux tube in SU(2) lattice gauge theory at high temperature
Chagdaa, S.; Galsandorj, E.; Laermann, E.; Purev, B.
2018-02-01
We study the profiles of the flux tube between a static quark and an antiquark in quenched SU(2) lattice gauge theory at temperatures around the deconfinement phase transition. The physical width of the flux tube and the string tension have been determined from the transverse profiles and the q\\bar{q} potential, respectively. Exploiting the computational power of a GPU accelerator in our flux tube investigation, we achieve much higher statistics through which we can increase the signal to noise ratio of our observables in the simulation. This has allowed the investigation of larger lattices as well as larger separations between the quarks than in our previous work. The improved accuracy gives us better results for the width and the string tension. The physical width of the flux tube increases with the temperature up to around T c while keeping its increasing dependence on the q\\bar{q} separation. The string tension results are compared for two different sizes of the lattice. As the lattice becomes larger and finer together with the improved precision, the temperature dependent string tension tends to have a smaller value than the previous one.
Group theoretical methods in Physics
Energy Technology Data Exchange (ETDEWEB)
Olmo, M.A. del; Santander, M.; Mateos Guilarte, J.M. (eds.) (Universidad de Valladolid. Facultad de Ciencias. Valladolid (Spain))
1993-01-01
The meeting had 102 papers. These was distributed in following areas: -Quantum groups,-Integrable systems,-Physical Applications of Group Theory,-Mathematical Results,-Geometry, Topology and Quantum Field Theory,-Super physics,-Super mathematics,-Atomic, Molecular and Condensed Matter Physics. Nuclear and Particle Physics,-Symmetry and Foundations of classical and Quantum mechanics.
Energy Technology Data Exchange (ETDEWEB)
Loewdin, P.; Calais, J.L.; Goscinski, O.
1976-12-01
Contents: Combination of special relativity and quantum mechanics; Trace algebra and chemical kinetics; Characterization of truncated basis sets by means of error quotients; General spin orbitals in Hartree-Fock theory; Cohesive properties of ionic crystals; and Description of ionization and excitation by means of transition operators.
Chattaraj, Pratim Kumar
2010-01-01
The application of quantum mechanics to many-particle systems has been an active area of research in recent years as researchers have looked for ways to tackle difficult problems in this area. The quantum trajectory method provides an efficient computational technique for solving both stationary and time-evolving states, encompassing a large area of quantum mechanics. Quantum Trajectories brings the expertise of an international panel of experts who focus on the epistemological significance of quantum mechanics through the quantum theory of motion.Emphasizing a classical interpretation of quan
Bialynicki-Birula, I; Ter Haar, D
1975-01-01
Quantum Electrodynamics focuses on the formulation of quantum electrodynamics (QED) in its most general and most abstract form: relativistic quantum field theory. It describes QED as a program, rather than a closed theory, that rests on the theory of the quantum Maxwellian field interacting with given (external) classical sources of radiation and on the relativistic quantum mechanics of electrons interacting with a given (external) classical electromagnetic field.Comprised of eight chapters, this volume begins with an introduction to the fundamental principles of quantum theory formulated in a
Blaise, Paul
2011-01-01
An invaluable reference for an overall but simple approach to the complexity of quantum mechanics viewed through quantum oscillators Quantum oscillators play a fundamental role in many areas of physics; for instance, in chemical physics with molecular normal modes, in solid state physics with phonons, and in quantum theory of light with photons. Quantum Oscillators is a timely and visionary book which presents these intricate topics, broadly covering the properties of quantum oscillators which are usually dispersed in the literature at varying levels of detail and often combined with other p
Dynamics of anisotropies close to a cosmological bounce in quantum gravity
de Cesare, Marco; Oriti, Daniele; Pithis, Andreas G. A.; Sakellariadou, Mairi
2018-01-01
We study the dynamics of perturbations representing deviations from perfect isotropy in the context of the emergent cosmology obtained from the group field theory formalism for quantum gravity. Working in the mean field approximation of the group field theory formulation of the Lorentzian EPRL model, we derive the equations of motion for such perturbations to first order. We then study these equations around a specific simple isotropic background, characterised by the fundamental representation of SU(2) , and in the regime of the effective cosmological dynamics corresponding to the bouncing region replacing the classical singularity, well approximated by the free GFT dynamics. In this particular example, we identify a region in the parameter space of the model such that perturbations can be large at the bounce but become negligible away from it, i.e. when the background enters the non-linear regime. We also study the departures from perfect isotropy by introducing specific quantities, such as the surface-area-to-volume ratio and the effective volume per quantum, which make them quantitative.
Measuring space-group symmetry fractionalization in Z2 spin liquids
Zaletel, Michael P.; Lu, Yuan-Ming; Vishwanath, Ashvin
2017-11-01
The interplay of symmetry and topological order leads to a variety of distinct phases of matter, the symmetry enriched topological (SET) phases. Here we discuss physical observables that distinguish different SETs in the context of Z2 quantum spin liquids with SU(2) spin rotation invariance. We focus on the cylinder geometry, and show that ground-state quantum numbers for different topological sectors are robust invariants which can be used to identify the SET phase. More generally, these invariants are related to 1D symmetry protected topological phases when viewing the cylinder geometry as a 1D spin chain. In particular, we show that the kagome spin liquid SET can be determined by measurements on one ground state, by wrapping the kagome in a few different ways on the cylinder. In addition to guiding numerical studies, this approach provides a transparent way to connect bosonic and fermionic mean-field theories of spin liquids. When fusing quasiparticles, it correctly predicts nontrivial phase factors for combining their space group quantum numbers.
Quantum robots and quantum computers
Energy Technology Data Exchange (ETDEWEB)
Benioff, P.
1998-07-01
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and systems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with different environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.
Energy Technology Data Exchange (ETDEWEB)
Zurek, Wojciech H [Los Alamos National Laboratory
2008-01-01
Quantum Darwinism - proliferation, in the environment, of multiple records of selected states of the system (its information-theoretic progeny) - explains how quantum fragility of individual state can lead to classical robustness of their multitude.
Gisin, Nicolas; Ribordy, Grégoire; Tittel, Wolfgang; Zbinden, Hugo
2002-01-01
Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.
Intrinsic Time Quantum Gravity
Yu, Hoi Lai
2016-01-01
Correct identification of the true gauge symmetry of General Relativity being 3d spatial diffeomorphism invariant(3dDI) (not the conventional infinite tensor product group with principle fibre bundle structure), together with intrinsic time extracted from clean decomposition of the canonical structure yields a self-consistent theory of quantum gravity. A new set of fundamental commutation relations is also presented. The basic variables are the eight components of the unimodular part of the spatial dreibein and eight SU(3) generators which correspond to Klauder's momentric variables that characterize a free theory of quantum gravity. The commutation relations are not canonical, but have well defined group theoretical meanings. All fundamental entities are dimensionless; and the quantum wave functionals are preferentially in the dreibein representation. The successful quantum theory of gravity involves only broad spectrum of knowledge and deep insights but no exotic idea.
Esteban Guevara Hidalgo
2006-01-01
The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that were described before through the replicator dynamics. Quantum mechanics could be used to explain more correctly biological and economical processes and even it could encloses theories like games and evolutionary dynamics. This could make quantum mechanics a...
S. Fehr (Serge)
2010-01-01
textabstractQuantum cryptography makes use of the quantum-mechanical behavior of nature for the design and analysis of cryptographic schemes. Optimally (but not always), quantum cryptography allows for the design of cryptographic schemes whose security is guaranteed solely by the laws of nature.
Principles and methods of quantum information technologies
Semba, Kouichi
2016-01-01
This book presents the research and development-related results of the “FIRST” Quantum Information Processing Project, which was conducted from 2010 to 2014 with the support of the Council for Science, Technology and Innovation of the Cabinet Office of the Government of Japan. The project supported 33 research groups and explored five areas: quantum communication, quantum metrology and sensing, coherent computing, quantum simulation, and quantum computing. The book is divided into seven main sections. Parts I through V, which consist of twenty chapters, focus on the system and architectural aspects of quantum information technologies, while Parts VI and VII, which consist of eight chapters, discuss the superconducting quantum circuit, semiconductor spin and molecular spin technologies. Readers will be introduced to new quantum computing schemes such as quantum annealing machines and coherent Ising machines, which have now arisen as alternatives to standard quantum computers and are designed to successf...
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
Quantum cluster algebras and quantum nilpotent algebras.
Goodearl, Kenneth R; Yakimov, Milen T
2014-07-08
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein-Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405-455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337-397] for the case of symmetric Kac-Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1-52] associated with double Bruhat cells coincide with the corresponding cluster algebras.
Zurek, Wojciech Hubert
2009-03-01
Quantum Darwinism describes the proliferation, in the environment, of multiple records of selected states of a quantum system. It explains how the quantum fragility of a state of a single quantum system can lead to the classical robustness of states in their correlated multitude; shows how effective `wave-packet collapse' arises as a result of the proliferation throughout the environment of imprints of the state of the system; and provides a framework for the derivation of Born's rule, which relates the probabilities of detecting states to their amplitudes. Taken together, these three advances mark considerable progress towards settling the quantum measurement problem.
Moulick, Subhayan Roy; Panigrahi, Prasanta K.
2016-06-01
We propose the idea of a quantum cheque scheme, a cryptographic protocol in which any legitimate client of a trusted bank can issue a cheque, that cannot be counterfeited or altered in anyway, and can be verified by a bank or any of its branches. We formally define a quantum cheque and present the first unconditionally secure quantum cheque scheme and show it to be secure against any no-signalling adversary. The proposed quantum cheque scheme can been perceived as the quantum analog of Electronic Data Interchange, as an alternate for current e-Payment Gateways.
Clothed Particles in Quantum Electrodynamics and Quantum Chromodynamics
Directory of Open Access Journals (Sweden)
Shebeko Alexander
2016-01-01
Full Text Available The notion of clothing in quantum field theory (QFT, put forward by Greenberg and Schweber and developed by M. Shirokov, is applied in quantum electrodynamics (QED and quantum chromodynamics (QCD. Along the guideline we have derived a novel analytic expression for the QED Hamiltonian in the clothed particle representation (CPR. In addition, we are trying to realize this notion in QCD (to be definite for the gauge group SU(3 when drawing parallels between QCD and QED.
Mathematical foundation of quantum mechanics
Parthasarathy, K R
2005-01-01
This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations ...
Quantum coherence versus quantum uncertainty
Luo, Shunlong; Sun, Yuan
2017-08-01
The notion of measurement is of both foundational and instrumental significance in quantum mechanics, and coherence destroyed by measurements (decoherence) lies at the very heart of quantum to classical transition. Qualitative aspects of this spirit have been widely recognized and analyzed ever since the inception of quantum theory. However, axiomatic and quantitative investigations of coherence are attracting great interest only recently with several figures of merit for coherence introduced [Baumgratz, Cramer, and Plenio, Phys. Rev. Lett. 113, 140401 (2014), 10.1103/PhysRevLett.113.140401]. While these resource theoretic approaches have many appealing and intuitive features, they rely crucially on various notions of incoherent operations which are sophisticated, subtle, and not uniquely defined, as have been critically assessed [Chitambar and Gour, Phys. Rev. Lett. 117, 030401 (2016), 10.1103/PhysRevLett.117.030401]. In this paper, we elaborate on the idea that coherence and quantum uncertainty are dual viewpoints of the same quantum substrate, and address coherence quantification by identifying coherence of a state (with respect to a measurement) with quantum uncertainty of a measurement (with respect to a state). Consequently, coherence measures may be set into correspondence with measures of quantum uncertainty. In particular, we take average quantum Fisher information as a measure of quantum uncertainty, and introduce the corresponding measure of coherence, which is demonstrated to exhibit desirable properties. Implications for interpreting quantum purity as maximal coherence, and quantum discord as minimal coherence, are illustrated.
Relativistic quantum mechanics
Horwitz, Lawrence P
2015-01-01
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...
Supersymmetric symplectic quantum mechanics
de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.
2018-02-01
Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.
Palaniappan, Kumaranand
2009-06-23
The synthesis of H/thiol terminated P3HT from Br/allyl-terminated P3HT precursor was analyzed. The photovoltaic response of blends were prepared of H/thiol terminated P3HT with spherical CdSe quantum dots(QD) and compares the results with regioregular H/Br and Br/aryl-terminated P3HT. Phase segregation was carried by mixing relatively polar pyridine treated CdSe QD with nonpolar P3HT. The experiment revealed that a high loading of CdSe is necessary for an efficient charge transport and different loading ratios of CdSe has been investigated to correlate the photovoltaic response as a function of ration between donor H/thiol-P3ht polymer and acceptor Cdse QD. The results show that H/Br-P3HT, H/thiol- and Br/allyl-terminated P3HT exhibits better performance and Cdse quantum dots were used to obtain results.
Quantum games as quantum types
Delbecque, Yannick
In this thesis, we present a new model for higher-order quantum programming languages. The proposed model is an adaptation of the probabilistic game semantics developed by Danos and Harmer [DH02]: we expand it with quantum strategies which enable one to represent quantum states and quantum operations. Some of the basic properties of these strategies are established and then used to construct denotational semantics for three quantum programming languages. The first of these languages is a formalisation of the measurement calculus proposed by Danos et al. [DKP07]. The other two are new: they are higher-order quantum programming languages. Previous attempts to define a denotational semantics for higher-order quantum programming languages have failed. We identify some of the key reasons for this and base the design of our higher-order languages on these observations. The game semantics proposed in this thesis is the first denotational semantics for a lambda-calculus equipped with quantum types and with extra operations which allow one to program quantum algorithms. The results presented validate the two different approaches used in the design of these two new higher-order languages: a first one where quantum states are used through references and a second one where they are introduced as constants in the language. The quantum strategies presented in this thesis allow one to understand the constraints that must be imposed on quantum type systems with higher-order types. The most significant constraint is the fact that abstraction over part of the tensor product of many unknown quantum states must not be allowed. Quantum strategies are a new mathematical model which describes the interaction between classical and quantum data using system-environment dialogues. The interactions between the different parts of a quantum system are described using the rich structure generated by composition of strategies. This approach has enough generality to be put in relation with other
Group Theoretical Properties and Band Structure of the Lamé Hamiltonian
Li, H; Iachello, Francesco; Li, Hui; Kusnezov, Dimitri
2000-01-01
We study the group theoretical properties of the Lamé equation and its relation to su(1,1) and su(2). We compute the band structure, dispersion relation and transfer matrix and discuss the dynamical symmetry limits.
Levy, Amikam; Diósi, Lajos; Kosloff, Ronnie
2016-05-01
In this work we present the concept of a quantum flywheel coupled to a quantum heat engine. The flywheel stores useful work in its energy levels, while additional power is extracted continuously from the device. Generally, the energy exchange between a quantum engine and a quantized work repository is accompanied by heat, which degrades the charging efficiency. Specifically when the quantum harmonic oscillator acts as a work repository, quantum and thermal fluctuations dominate the dynamics. Quantum monitoring and feedback control are applied to the flywheel in order to reach steady state and regulate its operation. To maximize the charging efficiency one needs a balance between the information gained by measuring the system and the information fed back to the system. The dynamics of the flywheel are described by a stochastic master equation that accounts for the engine, the external driving, the measurement, and the feedback operations.
Braun, Daniel; Giraud, Olivier; Braun, Peter A.
2010-03-01
We introduce and study a measure of ``quantumness'' of a quantum state based on its Hilbert-Schmidt distance from the set of classical states. ``Classical states'' were defined earlier as states for which a positive P-function exists, i.e. they are mixtures of coherent states [1]. We study invariance properties of the measure, upper bounds, and its relation to entanglement measures. We evaluate the quantumness of a number of physically interesting states and show that for any physical system in thermal equilibrium there is a finite critical temperature above which quantumness vanishes. We then use the measure for identifying the ``most quantum'' states. Such states are expected to be potentially most useful for quantum information theoretical applications. We find these states explicitly for low-dimensional spin-systems, and show that they possess beautiful, highly symmetric Majorana representations. [4pt] [1] Classicality of spin states, Olivier Giraud, Petr Braun, and Daniel Braun, Phys. Rev. A 78, 042112 (2008)
Khan, Shabbir A
2013-01-01
Quantum plasma physics is a rapidly evolving research field with a very inter-disciplinary scope of potential applications, ranging from nano-scale science in condensed matter to the vast scales of astrophysical objects. The theoretical description of quantum plasmas relies on various approaches, microscopic or macroscopic, some of which have obvious relation to classical plasma models. The appropriate model should, in principle, incorporate the quantum mechanical effects such as diffraction, spin statistics and correlations, operative on the relevant scales. However, first-principle approaches such as quantum Monte Carlo and density functional theory or quantum-statistical methods such as quantum kinetic theory or non-equilibrium Green's functions require substantial theoretical and computational efforts. Therefore, for selected problems, alternative simpler methods have been put forward. In particular, the collective behavior of many-body systems is usually described within a self-consistent scheme of parti...
Gilbert, Gerald; Hamrick, Michael
2013-01-01
This book provides a detailed account of the theory and practice of quantum cryptography. Suitable as the basis for a course in the subject at the graduate level, it crosses the disciplines of physics, mathematics, computer science and engineering. The theoretical and experimental aspects of the subject are derived from first principles, and attention is devoted to the practical development of realistic quantum communications systems. The book also includes a comprehensive analysis of practical quantum cryptography systems implemented in actual physical environments via either free-space or fiber-optic cable quantum channels. This book will be a valuable resource for graduate students, as well as professional scientists and engineers, who desire an introduction to the field that will enable them to undertake research in quantum cryptography. It will also be a useful reference for researchers who are already active in the field, and for academic faculty members who are teaching courses in quantum information s...
Busch, Paul; Pellonpää, Juha-Pekka; Ylinen, Kari
2016-01-01
This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann’s classic treatise with this title. Fundamental non-classical features of quantum mechanics—indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality—are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4....
Stapp, Henry
2009-01-01
Robert Griffiths has recently addressed, within the framework of a 'consistent quantum theory' that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises some essentially classical-physics-type assumptions that are fundamentally incompatible with the precepts of quantum physics. O...
Peguiron, J.
1997-01-01
In this thesis, ratchet systems operating in the quantum regime are investigated. Ratchet systems, also known as Brownian motors, are periodic systems presenting an intrinsic asymmetry which can be exploited to extract work out of unbiased forces. As a model for ratchet systems, we consider the motion of a particle in a one-dimensional periodic and asymmetric potential, interacting with a thermal environment, and subject to an unbiased driving force. In quantum ratchets, intrinsic quantum flu...
Experimental realization of quantum zeno dynamics.
Schäfer, F; Herrera, I; Cherukattil, S; Lovecchio, C; Cataliotti, F S; Caruso, F; Smerzi, A
2014-01-01
It is generally impossible to probe a quantum system without disturbing it. However, it is possible to exploit the back action of quantum measurements and strong couplings to tailor and protect the coherent evolution of a quantum system. This is a profound and counterintuitive phenomenon known as quantum Zeno dynamics. Here we demonstrate quantum Zeno dynamics with a rubidium Bose-Einstein condensate in a five-level Hilbert space. We harness measurements and strong couplings to dynamically disconnect different groups of quantum states and constrain the atoms to coherently evolve inside a two-level subregion. In parallel to the foundational importance due to the realization of a dynamical superselection rule and the theory of quantum measurements, this is an important step forward in protecting and controlling quantum dynamics and, broadly speaking, quantum information processing.
Fractional statistics and quantum theory
Khare, Avinash
1997-01-01
This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f
Quantum information and computation
Bub, Jeffrey
2005-01-01
This article deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information sheds new light on the conceptual problems of quantum mechanics.
Barnett, Stephen M
2009-01-01
Quantum information- the subject- is a new and exciting area of science, which brings together physics, information theory, computer science and mathematics. "Quantum Information"- the book- is based on two successful lecture courses given to advanced undergraduate and beginning postgraduate students in physics. The intention is to introduce readers at this level to the fundamental, but offer rather simple, ideas behind ground-breaking developments including quantum cryptography,teleportation and quantum computing. The text is necessarily rather mathematical in style, but the mathema
Vogel, Werner
2006-01-01
This is the third, revised and extended edition of the acknowledged "Lectures on Quantum Optics" by W. Vogel and D.-G. Welsch.It offers theoretical concepts of quantum optics, with special emphasis on current research trends. A unified concept of measurement-based nonclassicality and entanglement criteria and a unified approach to medium-assisted electromagnetic vacuum effects including Van der Waals and Casimir Forces are the main new topics that are included in the revised edition. The rigorous development of quantum optics in the context of quantum field theory and the attention to details makes the book valuable to graduate students as well as to researchers
Focus on gravitational quantum physics
Aspelmeyer, Marcus; Brukner, Časlav; Giulini, Domenico; Milburn, Gerard
2017-05-01
The interplay between quantum theory and gravity remains one of the least explored fields of physics. The current ‘focus on’ collection summarises experimental and theoretical results from many of the leading groups around the world on the research of phenomena which cannot be explained without involving both quantum theory and gravitational physics.
Quantum physics without quantum philosophy
Energy Technology Data Exchange (ETDEWEB)
Duerr, Detlef [Muenchen Univ. (Germany). Mathematisches Inst.; Goldstein, Sheldon [Rutgers State Univ., Piscataway, NJ (United States). Dept. of Mathematics; Zanghi, Nino [Genova Univ. (Italy); Istituto Nazionale Fisica Nucleare, Genova (Italy)
2013-02-01
Integrates and comments on the authors' seminal papers in the field. Emphasizes the natural way in which quantum phenomena emerge from the Bohmian picture. Helps to answer many of the objections raised to Bohmian quantum mechanics. Useful overview and summary for newcomers and students. It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schroedinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Liu, Cheng-Cheng; Wang, Dong; Sun, Wen-Yang; Ye, Liu
2017-10-01
In this paper, we investigate the relation among local quantum coherence, quantum uncertainty, and the nonlocal advantage of quantum coherence based on skew information and quantum phase transition in the transverse Ising model by exploring the quantum renormalization group (QRG) method. The results reveal that the amount of the local quantum uncertainty is equal to the local quantum coherence corresponding to the local observable {{σ }z} in the model, which can be generalized to a multipartite system. Moreover, the nonlocal advantage of quantum coherence is investigated, and we found that regardless of the value of the external magnet field and the number of QRG iterations, the quantum coherence of the subsystem was steerable, which is not only suitable for the two sites of the block, but also for the nearest-neighbor blocks in the long-ranged ferromagnetic phase. However, as the system becomes large enough, the quantum coherence of the subsystem is not steerable in the paramagnetic phase. Additionally, the QRG implementation of quantum coherence and uncertainty are effective and feasible to detect the quantum critical points associated with quantum phase transitions. We also make use of the QRG method to analyze the thermodynamic limit of the current model and the emergence of the nonanalytic and scaling behaviors of the nonlocal advantage of quantum coherence.
Rovelli, Carlo
2008-01-01
The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler's "spacetime foam" intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n-point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.
Directory of Open Access Journals (Sweden)
Rovelli Carlo
2008-07-01
Full Text Available The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler’s “spacetime foam” intuition. (iii Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv A derivation of the Bekenstein–Hawking black-hole entropy. (v Low-energy calculations, yielding n-point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.
Quantum computer games: quantum minesweeper
Gordon, Michal; Gordon, Goren
2010-07-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical minesweeper the goal of the game is to discover all the mines laid out on a board without triggering them, in the quantum version there are several classical boards in superposition. The goal is to know the exact quantum state, i.e. the precise layout of all the mines in all the superposed classical boards. The player can perform three types of measurement: a classical measurement that probabilistically collapses the superposition; a quantum interaction-free measurement that can detect a mine without triggering it; and an entanglement measurement that provides non-local information. The application of the concepts taught by quantum minesweeper to one-way quantum computing are also presented.
Quantum Physics Without Quantum Philosophy
Dürr, Detlef; Zanghì, Nino
2013-01-01
It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrödinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Visual Tools for Quantum Mechanics Education
Bernd Thaller
2006-01-01
We present the project Visual Quantum Mechanics, which uses computer-generated visualizations and animations to redefine content and quality of quantum-mechanical education at all levels. Main target group have been students of theoretical physics at universities, but more recently, we have developed learning objects for use at high schools. We describe the reasons for a visual approach to quantum mechanics and some specific methods for the visualization of quantum-mechanical objects.
Visual Tools for Quantum Mechanics Education
Directory of Open Access Journals (Sweden)
Bernd Thaller
2006-07-01
Full Text Available We present the project Visual Quantum Mechanics, which uses computer-generated visualizations and animations to redefine content and quality of quantum-mechanical education at all levels. Main target group have been students of theoretical physics at universities, but more recently, we have developed learning objects for use at high schools. We describe the reasons for a visual approach to quantum mechanics and some specific methods for the visualization of quantum-mechanical objects.
Quantum critical phase with infinite projected entangled paired states
Poilblanc, Didier; Mambrini, Matthieu
2017-07-01
A classification of SU(2)-invariant projected entangled paired states (PEPS) on the square lattice, based on a unique site tensor, has been recently introduced by Mambrini et al. [M. Mambrini, R. Orús, and D. Poilblanc, Phys. Rev. B 94, 205124 (2016), 10.1103/PhysRevB.94.205124]. It is not clear whether such SU(2)-invariant PEPS can either (i) exhibit long-range magnetic order (such as in the Néel phase) or (ii) describe a genuine quantum critical point (QCP) or quantum critical phase (QCPh) separating two ordered phases. Here, we identify a specific family of SU(2)-invariant PEPS of the classification which provides excellent variational energies for the J1-J2 frustrated Heisenberg model, especially at J2=0.5 , corresponding to the approximate location of the QCP or QCPh separating the Néel phase from a dimerized phase. The PEPS are built from virtual states belonging to the 1/2⊗N⊕0 SU(2) representation, i.e., with N "colors" of virtual spin-1/2 . Using a full-update infinite-PEPS approach directly in the thermodynamic limit, based on the corner transfer matrix renormalization algorithm supplemented by a conjugate gradient optimization scheme, we provide evidence of (i) the absence of magnetic order and of (ii) diverging correlation lengths (i.e., showing no sign of saturation with increasing environment dimension) in both the singlet and triplet channels, when the number of colors N ≥3 . We argue that such a PEPS gives a qualitative description of the QCP or QCPh of the J1-J2 model.
Quantum complexity of graph and algebraic problems
Energy Technology Data Exchange (ETDEWEB)
Doern, Sebastian
2008-02-04
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Steffen, Matthias
Solving computational problems require resources such as time, memory, and space. In the classical model of computation, computational complexity theory has categorized problems according to how difficult it is to solve them as the problem size increases. Remarkably, a quantum computer could solve certain problems using fundamentally fewer resources compared to a conventional computer, and therefore has garnered significant attention. Yet because of the delicate nature of entangled quantum states, the construction of a quantum computer poses an enormous challenge for experimental and theoretical scientists across multi-disciplinary areas including physics, engineering, materials science, and mathematics. While the field of quantum computing still has a long way to grow before reaching full maturity, state-of-the-art experiments on the order of 10 qubits are beginning to reach a fascinating stage at which they can no longer be emulated using even the fastest supercomputer. This raises the hope that small quantum computer demonstrations could be capable of approximately simulating or solving problems that also have practical applications. In this talk I will review the concepts behind quantum computing, and focus on the status of superconducting qubits which includes steps towards quantum error correction and quantum simulations.
Baaquie, Belal E.
2004-11-01
Financial mathematics is currently almost completely dominated by stochastic calculus. Presenting a completely independent approach, this book applies the mathematical and conceptual formalism of quantum mechanics and quantum field theory (with particular emphasis on the path integral) to the theory of options and to the modeling of interest rates. Many new results, accordingly, emerge from the author's perspective.
Kiefer, Claus
2012-01-01
The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction - the direct quantisation of Einstein's general theory of relativity and string theory - are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantization of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantization, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of stri...
Rae, Alastair I M
2016-01-01
A Thorough Update of One of the Most Highly Regarded Textbooks on Quantum Mechanics Continuing to offer an exceptionally clear, up-to-date treatment of the subject, Quantum Mechanics, Sixth Edition explains the concepts of quantum mechanics for undergraduate students in physics and related disciplines and provides the foundation necessary for other specialized courses. This sixth edition builds on its highly praised predecessors to make the text even more accessible to a wider audience. It is now divided into five parts that separately cover broad topics suitable for any general course on quantum mechanics. New to the Sixth Edition * Three chapters that review prerequisite physics and mathematics, laying out the notation, formalism, and physical basis necessary for the rest of the book * Short descriptions of numerous applications relevant to the physics discussed, giving students a brief look at what quantum mechanics has made possible industrially and scientifically * Additional end-of-chapter problems with...
Time Asymmetric Quantum Mechanics
Directory of Open Access Journals (Sweden)
Arno R. Bohm
2011-09-01
Full Text Available The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1 for states or the Heisenberg equation (6a for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus and observables (defined by a registration apparatus (detector. If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t_0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.
Energy Technology Data Exchange (ETDEWEB)
Smith, Jeremy C [ORNL; Topham, Christopher [University of Heidelberg
2007-01-01
Geometric descriptions of nonideal interresidue hydrogen bonding and backbone-base water bridging in the minor groove are established in terms of polyamide backbone carbonyl group orientation from analyses of residue junction conformers in experimentally determined peptide nucleic acid (PNA) complexes. Two types of interresidue hydrogen bonding are identified in PNA conformers in heteroduplexes with nucleic acids that adopt A-like base pair stacking. Quantum chemical calculations on the binding of a water molecule to an O2 base atom in glycine-based PNA thymine dimers indicate that junctions modeled with P-form backbone conformations are lower in energy than a dimer comprising the predominant conformation observed in A-like helices. It is further shown in model systems that PNA analogs based on D-lysine are better able to preorganize in a conformation exclusive to P-form helices than is glycine-based PNA. An intrinsic preference for this conformation is also exhibited by positively charged chiral PNA dimers carrying 3-amino-D-alanine or 4-aza-D-leucine residue units that provide for additional rigidity by side-chain hydrogen bonding to the backbone carbonyl oxygen. Structural modifications stabilizing P-form helices may obviate the need for large heterocycles to target DNA pyrimidine bases via PNADNA-PNA triplex formation. Quantum chemical modeling methods are used to propose candidate PNA Hoogsteen strand designs.
Quantum chromodynamics with advanced computing
Energy Technology Data Exchange (ETDEWEB)
Kronfeld, Andreas S.; /Fermilab
2008-07-01
We survey results in lattice quantum chromodynamics from groups in the USQCD Collaboration. The main focus is on physics, but many aspects of the discussion are aimed at an audience of computational physicists.
Cariolaro, Gianfranco
2015-01-01
This book demonstrates that a quantum communication system using the coherent light of a laser can achieve performance orders of magnitude superior to classical optical communications Quantum Communications provides the Masters and PhD signals or communications student with a complete basics-to-applications course in using the principles of quantum mechanics to provide cutting-edge telecommunications. Assuming only knowledge of elementary probability, complex analysis and optics, the book guides its reader through the fundamentals of vector and Hilbert spaces and the necessary quantum-mechanical ideas, simply formulated in four postulates. A turn to practical matters begins with and is then developed by: · development of the concept of quantum decision, emphasizing the optimization of measurements to extract useful information from a quantum system; · general formulation of a transmitter–receiver system · particular treatment of the most popular quantum co...
DEFF Research Database (Denmark)
2007-01-01
-theorists, and to stimulate contacts between participants. Each of the first four days was dedicated to one area of research that has recently seen decisive progress: \\begin{itemize} \\item structure and classification of wonderful varieties, \\item finite reductive groups and character sheaves, \\item quantum cohomology......The workshop continued a series of Oberwolfach meetings on algebraic groups, started in 1971 by Tonny Springer and Jacques Tits who both attended the present conference. This time, the organizers were Michel Brion, Jens Carsten Jantzen, and Raphaël Rouquier. During the last years, the subject...... of algebraic groups (in a broad sense) has seen important developments in several directions, also related to representation theory and algebraic geometry. The workshop aimed at presenting some of these developments in order to make them accessible to a "general audience" of algebraic group...
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C Language
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Coecke, Bob; Kissinger, Aleks
2017-03-01
Preface; 1. Introduction; 2. Guide to reading this textbook; 3. Processes as diagrams; 4. String diagrams; 5. Hilbert space from diagrams; 6. Quantum processes; 7. Quantum measurement; 8. Picturing classical-quantum processes; 9. Picturing phases and complementarity; 10. Quantum theory: the full picture; 11. Quantum foundations; 12. Quantum computation; 13. Quantum resources; 14. Quantomatic; Appendix A. Some notations; References; Index.
A biosensing of Toxoplasma gondii DNA with CdTe/Fe3O4 dual functional quantum dot as reporter group
Liang, Chu; Xu, Shichao; Yang, Juan; Zhang, Jimei; Dai, Zhao; Sun, Bo; Sun, Shuqing; Feng, Tielin; Zi, Yan; Liu, Jingwei; Luo, Hao
2009-07-01
Toxoplasma gondii is an intestinal coccidium that parasitizes members of the cat family as definitive hosts and has a wide range of intermediate hosts. Infection is common in many warm-blooded animals, including humans, the early detection of Toxoplasma gondii was concerned in recent years. In the current research, we presented a fast, specific, and sensitive sensing probe to detect Toxoplasma gondii DNA based on mechanism of fluorescence energy transfer (FRET), and a magnetic-fluorescent CdTe/Fe3O4 core-shell quantum dots (mQDs) was utilized as energy donor, and a commercial quencher (BHQ-2) was used as energy acceptor, respectively. The CdTe/Fe3O4 mQDs were prepared by layer-by-layer (LBL) process at ambient temperature. The sensing probe was fabricated through labeling a stem-loop Toxoplasma gondii DNA oligonucleotide with mQDs at the 5' end and BHQ-2 at 3' end, respectively, and the resulting sensing probe can be simply isolated and purified from the reactant with a common magnet. Properties of mQDs and sensing probe were determined by transmission electron microscopy (TEM) and fluorescence spectrum (FS). The TEM data demonstrated that the size of mQDs was ~20nm. the FS data indicated fluorescence intensity (FI) was doubled after the complete complimentary target Toxoplasma gondii DNA was introduced comparing with the FI before addition of target Toxoplasma gondii DNA. Moreover, only weak FI change was observed when the target DNA with one-mismatch base pair was added, this result revealed the sensing probe has high sensitivity and specificity. The current sensing probe will has great potential applications in the life science and related research.
Quantum Cryptography Beyond Quantum Key Distribution
Broadbent, A.; Schaffner, C
2015-01-01
textabstractQuantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation, secure two- and multi-party computation and delegated quantum computation. Quantum cryptography also studies the limitations and challenges resulting from quantum adversaries—including the ...
Quantum simulations with circuit quantum electrodynamics
Romero, G.; Solano, E.; Lamata, L.
2016-01-01
Superconducting circuits have become a leading quantum technology for testing fundamentals of quantum mechanics and for the implementation of advanced quantum information protocols. In this chapter, we revise the basic concepts of circuit network theory and circuit quantum electrodynamics for the sake of digital and analog quantum simulations of quantum field theories, relativistic quantum mechanics, and many-body physics, involving fermions and bosons. Based on recent improvements in scalabi...
Powell, John L
2015-01-01
Suitable for advanced undergraduates, this thorough text focuses on the role of symmetry operations and the essentially algebraic structure of quantum-mechanical theory. Based on courses in quantum mechanics taught by the authors, the treatment provides numerous problems that require applications of theory and serve to supplement the textual material.Starting with a historical introduction to the origins of quantum theory, the book advances to discussions of the foundations of wave mechanics, wave packets and the uncertainty principle, and an examination of the Schrödinger equation that includ
Lowe, John P
1993-01-01
Praised for its appealing writing style and clear pedagogy, Lowe's Quantum Chemistry is now available in its Second Edition as a text for senior undergraduate- and graduate-level chemistry students. The book assumes little mathematical or physical sophistication and emphasizes an understanding of the techniques and results of quantum chemistry, thus enabling students to comprehend much of the current chemical literature in which quantum chemical methods or concepts are used as tools. The book begins with a six-chapter introduction of standard one-dimensional systems, the hydrogen atom,
Chowdhury, Sujaul
2014-01-01
This book presents comprehensive account of the course for undergraduate students with thorough and complete calculations. The book has been written with the notion that a wave is associated with a material particle i.e. wave and particle coexist. Heisenberg's uncertainty principle has been described in light of this. A chapter is dedicated to mathematical structure of Quantum Mechanics followed by applications to one-dimensional (1D) problems. Orbital and general angular momentum are treated in two separate chapters, the latter also treats addition of angular momentum. Quantum theory of scattering, matrix formulation of Quantum Mechanics variational method and WKB approximation method have also been discussed.
Quantum algorithmic information theory
Svozil, Karl
1995-01-01
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory. The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a two-port interferometer capa...
Kondo effect in triple quantum dots: interplay between continuous and discrete symmetries
Energy Technology Data Exchange (ETDEWEB)
Kikoin, K. [Department of Physics, Ben-Gurion University, Beer-Sheva, 84105 (Israel)]. E-mail: kikoin@bgumail.bgu.ac.il; Kuzmenko, T. [Department of Physics, Ben-Gurion University, Beer-Sheva, 84105 (Israel); Avishai, Y. [Department of Physics, Ben-Gurion University, Beer-Sheva, 84105 (Israel); Ilse Kats Center for Nano-Technology, Ben-Gurion University, Beer-Sheva, 84105 (Israel)
2006-05-01
The physics of Kondo effect and related phenomena in a triangular triple quantum dot (TTQD) is studied. A fascinating property of TTQD is the interplay between continuous SU(2) symmetry in spin space and discrete C{sub 3v} symmetry in real space. We show that this interplay is manifested in strong oscillations of conductance as a function of magnetic flux through TTQD due to interplay between Kondo and Aharonov-Bohm effect.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 16; Issue 9. Quantum Computation - Particle and Wave Aspects of Algorithms. Apoorva Patel. General Article Volume 16 ... Keywords. Boolean logic; computation; computational complexity; digital language; Hilbert space; qubit; superposition; Feynman.
Quantum correlations and distinguishability of quantum states
Energy Technology Data Exchange (ETDEWEB)
Spehner, Dominique [Université Grenoble Alpes and CNRS, Institut Fourier, F-38000 Grenoble, France and Laboratoire de Physique et Modélisation des Milieux Condensés, F-38000 Grenoble (France)
2014-07-15
A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination, quantum relative entropies, the Bures distance on the set of quantum states, the quantum Fisher information, the quantum Chernoff bound, bipartite entanglement, the quantum discord, and geometrical measures of quantum correlations. The article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them, and for mathematicians looking for an up-to-date introductory course on these subjects, which are mainly developed in the physics literature.
DEFF Research Database (Denmark)
Andersen, Ulrik Lund
2013-01-01
Further sensitivity improvements are required before advanced optical interferometers will be able to measure gravitational waves. A team has now shown that introducing quantum squeezing of light may help to detect these elusive waves.......Further sensitivity improvements are required before advanced optical interferometers will be able to measure gravitational waves. A team has now shown that introducing quantum squeezing of light may help to detect these elusive waves....
Schwarz, Albert
2014-01-01
One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if [P,Q]=const. If a pair of difference operators (K,L) obey the relation KL=const LK we say that they specify a discrete quantum curve. This terminology is prompted by well known results about commuting differential and difference operators, relating pairs of such operators with pairs of meromorphic functions on algebraic curves obeying some conditions. ...
Grunspan, C.
2002-01-01
This text gives some results about quantum torsors. Our starting point is an old reformulation of torsors recalled recently by Kontsevich. We propose an unification of the definitions of torsors in algebraic geometry and in Poisson geometry. Any quantum torsor is equipped with two comodule-algebra structures over Hopf algebras and these structures commute with each other. In the finite dimensional case, these two Hopf algebras share the same finite dimension. We show that any Galois extension...
CERN Bulletin
2013-01-01
On April Fools' Day, CERN Quantum Diaries blogger Pauline Gagnon held a giveaway of microscopic proportion. Up for grabs? Ten Higgs bosons, courtesy of CERN. Pauline announced the winners last week; let's see what they'll really be getting in the mail... Custom-made Particle Zoo Higgs bosons were sent out to the winners. Read more about the prize in the Quantum Diaries post "Higgs boson lottery: when CERN plays April Fools' jokes".
Symmetry and quantum mechanics
Corry, Scott
2016-01-01
This book offers an introduction to quantum mechanics for professionals, students, and others in the field of mathematics who have a minimal background in physics with an understanding of linear algebra and group theory. It covers such topics as Lie groups, algebras and their representations, and analysis (Hilbert space, distributions, the spectral Theorem, and the Stone-Von Neumann Theorem). The book emphasizes the role of symmetry and is useful to physicists as it provides a mathematical introduction to the topic.
Quantum entanglement and quantum computational algorithms
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 56; Issue 2-3. Quantum entanglement ... Arvind. Quantum information processing Volume 56 Issue 2-3 February-March 2001 pp 357-365 ... The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum ...
Quantum Computation and Quantum Spin Dynamics
Raedt, Hans De; Michielsen, Kristel; Hams, Anthony; Miyashita, Seiji; Saito, Keiji
2001-01-01
We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum
Logical independence and quantum randomness
Energy Technology Data Exchange (ETDEWEB)
Paterek, T; Kofler, J; Aspelmeyer, M; Zeilinger, A; Brukner, C [Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna (Austria); Prevedel, R; Klimek, P [Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna (Austria)], E-mail: tomasz.paterek@univie.ac.at
2010-01-15
We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.
Computing on quantum shared secrets
Ouyang, Yingkai; Tan, Si-Hui; Zhao, Liming; Fitzsimons, Joseph F.
2017-11-01
A (k ,n )-threshold secret-sharing scheme allows for a string to be split into n shares in such a way that any subset of at least k shares suffices to recover the secret string, but such that any subset of at most k -1 shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation securely on quantum shared secrets. We introduce a (n ,n )-quantum secret sharing scheme together with a set of algorithms that allow quantum circuits to be evaluated securely on the shared secret without the need to decode the secret. We consider a multipartite setting, with each participant holding a share of the secret. We show that if there exists at least one honest participant, no group of dishonest participants can recover any information about the shared secret, independent of their deviations from the algorithm.
Classical and quantum anisotropic Heisenberg antiferromagnets
Directory of Open Access Journals (Sweden)
W. Selke
2009-01-01
Full Text Available We study classical and quantum Heisenberg antiferromagnets with exchange anisotropy of XXZ-type and crystal field single-ion terms of quadratic and quartic form in a field. The magnets display a variety of phases, including the spin-flop (or, in the quantum case, spin-liquid and biconical (corresponding, in the quantum lattice gas description, to supersolid phases. Applying ground-state considerations, Monte Carlo and density matrix renormalization group methods, the impact of quantum effects and lattice dimension is analysed. Interesting critical and multicritical behaviour may occur at quantum and thermal phase transitions.
On a Quantum Theory of Relativity
González-Díaz, Pedro F.; Rozas-Fernández, Alberto
2017-09-01
As expressed in terms of classical coordinates, the inertial spacetime metric that contains quantum corrections deriving from a quantum potential defined from the quantum probability amplitude is obtained to be given as an elliptic integral of the second kind that does not satisfy Lorentz transformations but a generalised invariance quantum group. Based on this result, we introduce a new, alternative procedure to quantise Einstein general relativity where the metric is also given in terms of elliptic integrals and is free from the customary problems of the current quantum models. We apply the procedure to Schwarzschild black holes and briefly analyse the results.
Quantum computing: Quantum advantage deferred
Childs, Andrew M.
2017-12-01
A type of optics experiment called a boson sampler could be among the easiest routes to demonstrating the power of quantum computers. But recent work shows that super-classical boson sampling may be a long way off.
2D Multipartite Valence Bond States in Quantum Antiferromagnets
Rico, E
2007-01-01
A quantum anti-ferromagnetic spin-1 model is characterised on a 2D lattice with the following requirements: i) The Hamiltonian is made out of nearest neighbour interactions. ii) It is homogeneous, translational and rotational invariant. iii) The ground state is a real singlet state of SU(2) (non-chiral). iv) It has a local spin-1 representation. Along the way to characterise the system, connections with classical statistical mechanics and integrable models are explored. Finally, the relevance of the model in the physics of low dimensional anti-ferromagnetic Mott-Hubbard insulators is discussed.
Semiclassical Loop Quantum Gravity and Black Hole Thermodynamics
Directory of Open Access Journals (Sweden)
Arundhati Dasgupta
2013-02-01
Full Text Available In this article we explore the origin of black hole thermodynamics using semiclassical states in loop quantum gravity. We re-examine the case of entropy using a density matrix for a coherent state and describe correlations across the horizon due to SU(2 intertwiners. We further show that Hawking radiation is a consequence of a non-Hermitian term in the evolution operator, which is necessary for entropy production or depletion at the horizon. This non-unitary evolution is also rooted in formulations of irreversible physics.
Quantum Physics for Beginners.
Strand, J.
1981-01-01
Suggests a new approach for teaching secondary school quantum physics. Reviews traditional approaches and presents some characteristics of the three-part "Quantum Physics for Beginners" project, including: quantum physics, quantum mechanics, and a short historical survey. (SK)
Quantum Transmemetic Intelligence
Piotrowski, Edward W.; Sładkowski, Jan
The following sections are included: * Introduction * A Quantum Model of Free Will * Quantum Acquisition of Knowledge * Thinking as a Quantum Algorithm * Counterfactual Measurement as a Model of Intuition * Quantum Modification of Freud's Model of Consciousness * Conclusion * Acknowledgements * References
Quantum Phase Transitions in Quantum Dots
Rau, I. G.; Amasha, S.; Oreg, Y.; Goldhaber-Gordon, D.
2013-01-01
This review article describes theoretical and experimental advances in using quantum dots as a system for studying impurity quantum phase transitions and the non-Fermi liquid behavior at the quantum critical point.
Quantum Communication and Quantum Multivariate Polynomial Interpolation
Diep, Do Ngoc; Giang, Do Hoang
2017-09-01
The paper is devoted to the problem of multivariate polynomial interpolation and its application to quantum secret sharing. We show that using quantum Fourier transform one can produce the protocol for quantum secret sharing distribution.
Long distance quantum teleportation
Xia, Xiu-Xiu; Sun, Qi-Chao; Zhang, Qiang; Pan, Jian-Wei
2018-01-01
Quantum teleportation is a core protocol in quantum information science. Besides revealing the fascinating feature of quantum entanglement, quantum teleportation provides an ultimate way to distribute quantum state over extremely long distance, which is crucial for global quantum communication and future quantum networks. In this review, we focus on the long distance quantum teleportation experiments, especially those employing photonic qubits. From the viewpoint of real-world application, both the technical advantages and disadvantages of these experiments are discussed.
Non-Abelian spin liquid in a spin-one quantum magnet.
Grover, Tarun; Senthil, T
2011-08-12
We study a time-reversal invariant non-Abelian spin-liquid state in an SU(2) symmetric spin S=1 quantum magnet on a triangular lattice. The spin liquid is obtained by quantum disordering a noncollinear nematic state. We show that such a spin liquid cannot be obtained by the standard projective construction for spin liquids. We also study the phase transition between the spin liquid and the noncollinear nematic state and show that it cannot be described within the Landau-Ginzburg-Wilson paradigm.
SU(2)×U(1) gauge invariance and the shape of new physics in rare B decays.
Alonso, R; Grinstein, B; Martin Camalich, J
2014-12-12
New physics effects in B decays are routinely modeled through operators invariant under the strong and electromagnetic gauge symmetries. Assuming the scale for new physics is well above the electroweak scale, we further require invariance under the full standard model gauge symmetry group. Retaining up to dimension-six operators, we unveil new constraints between different new physics operators that are assumed to be independent in the standard phenomenological analyses. We illustrate this approach by analyzing the constraints on new physics from rare B(q) (semi-)leptonic decays.
Quantum Monte Carlo methods and strongly correlated electrons on honeycomb structures
Energy Technology Data Exchange (ETDEWEB)
Lang, Thomas C.
2010-12-16
In this thesis we apply recently developed, as well as sophisticated quantum Monte Carlo methods to numerically investigate models of strongly correlated electron systems on honeycomb structures. The latter are of particular interest owing to their unique properties when simulating electrons on them, like the relativistic dispersion, strong quantum fluctuations and their resistance against instabilities. This work covers several projects including the advancement of the weak-coupling continuous time quantum Monte Carlo and its application to zero temperature and phonons, quantum phase transitions of valence bond solids in spin-1/2 Heisenberg systems using projector quantum Monte Carlo in the valence bond basis, and the magnetic field induced transition to a canted antiferromagnet of the Hubbard model on the honeycomb lattice. The emphasis lies on two projects investigating the phase diagram of the SU(2) and the SU(N)-symmetric Hubbard model on the hexagonal lattice. At sufficiently low temperatures, condensed-matter systems tend to develop order. An exception are quantum spin-liquids, where fluctuations prevent a transition to an ordered state down to the lowest temperatures. Previously elusive in experimentally relevant microscopic two-dimensional models, we show by means of large-scale quantum Monte Carlo simulations of the SU(2) Hubbard model on the honeycomb lattice, that a quantum spin-liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. This unexpected quantum-disordered state is found to be a short-range resonating valence bond liquid, akin to the one proposed for high temperature superconductors. Inspired by the rich phase diagrams of SU(N) models we study the SU(N)-symmetric Hubbard Heisenberg quantum antiferromagnet on the honeycomb lattice to investigate the reliability of 1/N corrections to large-N results by means of numerically exact QMC simulations. We study the melting of phases
The standard model coupled to quantum gravitodynamics
Energy Technology Data Exchange (ETDEWEB)
Aldabe, Fermin
2017-01-15
We show that the renormalizable SO(4) x U(1) x SU(2) x SU(3) Yang-Mills coupled to matter and the Higgs field fits all the experimentally observed differential cross sections known in nature. This extended Standard Model reproduces the experimental gravitational differential cross sections without resorting to the graviton field and instead by exchanging SO(4) gauge fields. By construction, each SO(4) generator in quantum gravitodynamics does not commute with the Dirac gamma matrices. This produces additional interactions absent to non-Abelian gauge fields in the Standard Model. The contributions from these new terms yield differential cross sections consistent with the Newtonian and post-Newtonian interactions derived from General Relativity. Dimensional analysis of the Lagrangian shows that all its terms have total dimensionality four or less and therefore that all physical quantities in the theory renormalize by finite amounts. These properties make QGD the only renormalizable four-dimensional theory describing gravitational interactions. (orig.)
Ghosh, P K
2014-01-01
Quantum mechanics, designed for advanced undergraduate and graduate students of physics, mathematics and chemistry, provides a concise yet self-contained introduction to the formal framework of quantum mechanics, its application to physical problems and the interpretation of the theory. Starting with a review of some of the necessary mathematics, the basic concepts are carefully developed in the text. After building a general formalism, detailed treatment of the standard material - the harmonic oscillator, the hydrogen atom, angular momentum theory, symmetry transformations, approximation methods, identical particle and many-particle systems, and scattering theory - is presented. The concluding chapter discusses the interpretation of quantum mechanics. Some of the important topics discussed in the book are the rigged Hilbert space, deformation quantization, path integrals, coherent states, geometric phases, decoherene, etc. This book is characterized by clarity and coherence of presentation.
Bény, Cédric
2018-02-01
We propose a method for stably removing noise from measurements of a quantum many-body system. The question is cast to a linear inverse problem by using a quantum Fischer information metric as figure of merit. This requires the ability to compute the adjoint of the noise channel with respect to the metric, which can be done analytically when the metric is evaluated at a Gaussian (quasi-free) state. This approach can be applied effectively to n-point functions of a quantum field theory. For translation invariant noise, this yields a stable deconvolution method on the first moments of the field which differs from what one would obtain from a purely classical analysis.
Exner, Pavel
2015-01-01
This monograph explains the theory of quantum waveguides, that is, dynamics of quantum particles confined to regions in the form of tubes, layers, networks, etc. The focus is on relations between the confinement geometry on the one hand and the spectral and scattering properties of the corresponding quantum Hamiltonians on the other. Perturbations of such operators, in particular, by external fields are also considered. The volume provides a unique summary of twenty five years of research activity in this area and indicates ways in which the theory can develop further. The book is fairly self-contained. While it requires some broader mathematical physics background, all the basic concepts are properly explained and proofs of most theorems are given in detail, so there is no need for additional sources. Without a parallel in the literature, the monograph by Exner and Kovarik guides the reader through this new and exciting field.
Mullin, William J
2017-01-01
Quantum mechanics allows a remarkably accurate description of nature and powerful predictive capabilities. The analyses of quantum systems and their interpretation lead to many surprises, for example, the ability to detect the characteristics of an object without ever touching it in any way, via "interaction-free measurement," or the teleportation of an atomic state over large distances. The results can become downright bizarre. Quantum mechanics is a subtle subject that usually involves complicated mathematics -- calculus, partial differential equations, etc., for complete understanding. Most texts for general audiences avoid all mathematics. The result is that the reader misses almost all deep understanding of the subject, much of which can be probed with just high-school level algebra and trigonometry. Thus, readers with that level of mathematics can learn so much more about this fundamental science. The book starts with a discussion of the basic physics of waves (an appendix reviews some necessary class...
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Okumura, M; Onishi, H; Yamada, S; Machida, M, E-mail: okumura@riken.j
2010-11-01
We study non-equilibrium properties of one-dimensional Hubbard model by the density-matrix renormalization-group method. First, we demonstrate stability of 'doublon', which characterized by double occupation on a site due to the integrability of the model. Next, we present a kind of anomalous transport caused by the doublons created under strong non-equilibrium conditions in an optical lattice system regarded as an ideal testbed to investigate fundamental properties of the Hubbard model. Finally, we give a result on development of the pair correlation function in a strong non-equilibrium condition. This can be understood as a development of coherence among many excited doublons.
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Hyman, J.; Beyer, W.; Louck, J.; Metropolis, N.
1996-07-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Group theoretical methods are a powerful tool both in their applications to mathematics and to physics. The broad goal of this project was to use such methods to develop the implications of group (symmetry) structures underlying models of physical systems, as well as to broaden the understanding of simple models of chaotic systems. The main thrust was to develop further the complex mathematics that enters into many-particle quantum systems with special emphasis on the new directions in applied mathematics that have emerged and continue to surface in these studies. In this area, significant advances in understanding the role of SU(2) 3nj-coefficients in SU(3) theory have been made and in using combinatoric techniques in the study of generalized Schur functions, discovered during this project. In the context of chaos, the study of maps of the interval and the associated theory of words has led to significant discoveries in Galois group theory, to the classification of fixed points, and to the solution of a problem in the classification of DNA sequences.
Blind Quantum Signature with Blind Quantum Computation
Li, Wei; Shi, Ronghua; Guo, Ying
2017-04-01
Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.
Quantum scaling in many-body systems an approach to quantum phase transitions
Continentino, Mucio
2017-01-01
Quantum phase transitions are strongly relevant in a number of fields, ranging from condensed matter to cold atom physics and quantum field theory. This book, now in its second edition, approaches the problem of quantum phase transitions from a new and unifying perspective. Topics addressed include the concepts of scale and time invariance and their significance for quantum criticality, as well as brand new chapters on superfluid and superconductor quantum critical points, and quantum first order transitions. The renormalisation group in real and momentum space is also established as the proper language to describe the behaviour of systems close to a quantum phase transition. These phenomena introduce a number of theoretical challenges which are of major importance for driving new experiments. Being strongly motivated and oriented towards understanding experimental results, this is an excellent text for graduates, as well as theorists, experimentalists and those with an interest in quantum criticality.
Quantum Field Theory A Modern Perspective
Parameswaran Nair, V
2005-01-01
Quantum field theory, which started with Paul Dirac’s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity. Quantum Field Theory: A Modern Perspective presents Professor Nair’s view of certain topics in field theory loosely knit together as it gr...
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Degen, F.
1987-07-01
For an SU(2) Einstein-Yang-Mills-Higgs model they study the extreme wormhole solutions. They use an iterative method based on expansion in the radial distance N from the boundary of the hole. Here they present the nontrivial solutions of the first-order equations. They give useful information about existing extremal wormholes. Especially they note that although the zero-order solution which they use is abelian, this is not the case for all solutions of first-order equations. The method employed in solving these equations is to expand all first-order fields in the appropriate generalized harmonics. They find a nonabelian solution if the value of the Higgs scalar at the horizon is equal to the Planck mass and if the magnetic charge b and the electric charge e of the hole satisfy b = 1/e.
Rae, Alastair I M
2007-01-01
PREFACESINTRODUCTION The Photoelectric Effect The Compton Effect Line Spectra and Atomic Structure De Broglie Waves Wave-Particle Duality The Rest of This Book THE ONE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Time-Dependent Schrödinger Equation The Time-Independent Schrödinger Equation Boundary ConditionsThe Infinite Square Well The Finite Square Well Quantum Mechanical Tunneling The Harmonic Oscillator THE THREE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Wave Equations Separation in Cartesian Coordinates Separation in Spherical Polar Coordinates The Hydrogenic Atom THE BASIC POSTULATES OF QUANTUM MEC
Kottos, T.
2007-01-01
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wave function statistics. This operator is the analogue of the classical evolution operator on the graph. It allows us to establish a connection between the corresponding periodic orbits and the statistical properties of eigenvalues and eigenfunctions. Specifically, for the energy-averaged spectral form factor we derived an exact combinatorial expression which illustrate the role of correlations between families of isometric orbits. We also show that enhanced wave function localization due to the presence of short unstable periodic orbits and strong scarring can rely on completely different mechanisms
Bojowald, Martin
2006-01-01
A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum cosmology, item (2) is the quantum state of the cosmos. Hartle and Hawking have made the `no-boundary' proposal, that the wavefunction of the universe is given by a path integral over all compact Euclidean 4-dimensional geometries and matter fields that hav...
Buhrman, Harry
2006-01-01
École thématique; Quantum Information, Computation and Complexity * Programme at the Institut Henri Poincaré, January 4th – April 7th, 2006 * Organizers: Ph.Grangier, M.Santha and D.L.Shepelyansky * Lectures have been filmed by Peter Rapcan and Michal Sedlak from Bratislava with the support of the Marie Curie RTN "CONQUEST" A trimester at the Centre Emile Borel - Institut Henri Poincaré is devoted to modern developments in a rapidly growing field of quantum information and communication, quan...
Zagoskin, Alexandre
2015-01-01
Written by Dr Alexandre Zagoskin, who is a Reader at Loughborough University, Quantum Mechanics: A Complete Introduction is designed to give you everything you need to succeed, all in one place. It covers the key areas that students are expected to be confident in, outlining the basics in clear jargon-free English, and then providing added-value features like summaries of key ideas, and even lists of questions you might be asked in your exam. The book uses a structure that is designed to make quantum physics as accessible as possible - by starting with its similarities to Newtonian physics, ra
Linking topological quantum field theory and nonperturbative quantum gravity
Smolin, Lee
1995-11-01
Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory in which the pullback of the curvature to the boundary is self-dual (with a cosmological constant). A Hilbert space which describes all the information accessible by measuring the metric and connection induced in the boundary is constructed and is found to be the direct sum of the state spaces of all SU(2) Chern-Simon theories defined by all choices of punctures and representations on the spatial boundary S. The integer level k of Chern-Simons theory is found to be given by k=6π/G2Λ+α, where Λ is the cosmological constant and α is a CP breaking phase. Using these results, expectation values of observables which are functions of fields on the boundary may be evaluated in closed form. Given these results, it is natural to make the conjecture that the quantum states of the system are completely determined by measurements made on the boundary. One consequence of this is the Bekenstein bound, which says that once the two metric of the boundary has been measured, the subspace of the physical state space that describes the further information that may be obtained about the interior has finite dimension equal to the exponent of the area of the boundary, in Planck units, times a fixed constant. Finally, these results confirm both the categorical-theoretic ``ladder of dimensions'' picture of Crane and the holographic hypothesis of Susskind and 't Hooft.
Höhn, Philipp Andres; Wever, Christopher S. P.
2017-01-01
We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and define S 's state as O 's "catalog of knowledge" about S . From the rules we derive the state spaces for N elementary systems and show that (a) they coincide with the set of density matrices over an N -qubit Hilbert space C2N; (b) states evolve unitarily under the group PSU (2N) according to the von Neumann evolution equation; and (c) O 's binary questions correspond to projective Pauli operator measurements with outcome probabilities given by the Born rule. As a by-product, this results in a propositional formulation of quantum theory. Aside from offering an informational explanation for the theory's architecture, the reconstruction also unravels previously unnoticed structural insights. We show that, in a derived quadratic information measure, (d) qubits satisfy inequalities which bound the information content in any set of mutually complementary questions to 1 bit; and (e) maximal sets of mutually complementary questions for one and two qubits must carry precisely 1 bit of information in pure states. The latter relations constitute conserved informational charges which define the unitary groups and, together with their conservation conditions, the sets of pure quantum states. These results highlight information as a "charge of quantum theory" and the benefits of this informational approach. This work emphasizes the sufficiency of restricting to an observer's information to reconstruct the theory and completes the quantum reconstruction initiated in a companion paper (P. Höhn, arXiv:1412.8323).
Quantum gravity and quantum cosmology
Papantonopoulos, Lefteris; Siopsis, George; Tsamis, Nikos
2013-01-01
Quantum gravity has developed into a fast-growing subject in physics and it is expected that probing the high-energy and high-curvature regimes of gravitating systems will shed some light on how to eventually achieve an ultraviolet complete quantum theory of gravity. Such a theory would provide the much needed information about fundamental problems of classical gravity, such as the initial big-bang singularity, the cosmological constant problem, Planck scale physics and the early-time inflationary evolution of our Universe. While in the first part of this book concepts of quantum gravity are introduced and approached from different angles, the second part discusses these theories in connection with cosmological models and observations, thereby exploring which types of signatures of modern and mathematically rigorous frameworks can be detected by experiments. The third and final part briefly reviews the observational status of dark matter and dark energy, and introduces alternative cosmological models. ...
Quantum biological information theory
Djordjevic, Ivan B
2016-01-01
This book is a self-contained, tutorial-based introduction to quantum information theory and quantum biology. It serves as a single-source reference to the topic for researchers in bioengineering, communications engineering, electrical engineering, applied mathematics, biology, computer science, and physics. The book provides all the essential principles of the quantum biological information theory required to describe the quantum information transfer from DNA to proteins, the sources of genetic noise and genetic errors as well as their effects. Integrates quantum information and quantum biology concepts; Assumes only knowledge of basic concepts of vector algebra at undergraduate level; Provides a thorough introduction to basic concepts of quantum information processing, quantum information theory, and quantum biology; Includes in-depth discussion of the quantum biological channel modelling, quantum biological channel capacity calculation, quantum models of aging, quantum models of evolution, quantum models o...
Deconfined quantum criticality in SU(3) antiferromagnets on the triangular lattice
Pimenov, Dimitri; Punk, Matthias
2017-05-01
We propose field theories for a deconfined quantum critical point in SU(3) antiferromagnets on the triangular lattice. In particular we consider the continuous transition between a magnetic, three-sublattice color-ordered phase and a trimerized SU(3) singlet phase. Starting from the magnetically ordered state we derive a critical theory in terms of fractional bosonic degrees of freedom, in close analogy to the well-developed description of the SU(2) Néel—valence bond solid (VBS) transition on the square lattice. Our critical theory consists of three coupled C P2 models and we study its fixed point structure using a functional renormalization group approach in a suitable large N limit. We find a stable critical fixed point and estimate its critical exponents, thereby providing an example of deconfined criticality beyond the universality class of the C PN model. In addition we present a complementary route towards the critical field theory by studying topological defects of the trimerized SU(3) singlet phase.
2010-03-04
be required. In 2001, a breakthrough known as the KLM (Knill–Laflamme– Milburn13) scheme showed that scalable quantum computing is possible using only...and single-photon detection to induce interactions nondeterministically. In the past five years, the KLM scheme has moved from a mathematical proof
Raedt, Hans De; Binder, K; Ciccotti, G
1996-01-01
The purpose of this set of lectures is to introduce the general concepts that are at the basis of the computer simulation algorithms that are used to study the behavior of condensed matter quantum systems. The emphasis is on the underlying concepts rather than on specific applications. Topics
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Sassoli de Bianchi, Massimiliano, E-mail: autoricerca@gmail.com
2013-09-15
In a letter to Born, Einstein wrote [42]: “Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the ‘old one.’ I, at any rate, am convinced that He does not throw dice.” In this paper we take seriously Einstein’s famous metaphor, and show that we can gain considerable insight into quantum mechanics by doing something as simple as rolling dice. More precisely, we show how to perform measurements on a single die, to create typical quantum interference effects, and how to connect (entangle) two identical dice, to maximally violate Bell’s inequality. -- Highlights: •Rolling a die is a quantum process admitting a Hilbert space representation. •Rolling experiments with a single die can produce interference effects. •Two connected dice can violate Bell’s inequality. •Correlations need to be created by the measurement, to violate Bell’s inequality.
2016-03-24
semiconductors. Personnel Graduate students supported by this grant: Michael Gehl (Graduated with PhD in October 2015, now at Sandia... Ell , O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity.” Nature 432, 200-203 (2004
Directory of Open Access Journals (Sweden)
Alessandro Sergi
2009-06-01
Full Text Available A critical assessment of the recent developmentsof molecular biology is presented.The thesis that they do not lead to a conceptualunderstanding of life and biological systems is defended.Maturana and Varela's concept of autopoiesis is briefly sketchedand its logical circularity avoided by postulatingthe existence of underlying living processes,entailing amplification from the microscopic to the macroscopic scale,with increasing complexity in the passage from one scale to the other.Following such a line of thought, the currently accepted model of condensed matter, which is based on electrostatics and short-ranged forces,is criticized. It is suggested that the correct interpretationof quantum dispersion forces (van der Waals, hydrogen bonding, and so onas quantum coherence effects hints at the necessity of includinglong-ranged forces (or mechanisms for them incondensed matter theories of biological processes.Some quantum effects in biology are reviewedand quantum mechanics is acknowledged as conceptually important to biology since withoutit most (if not all of the biological structuresand signalling processes would not even exist. Moreover, it is suggested that long-rangequantum coherent dynamics, including electron polarization,may be invoked to explain signal amplificationprocess in biological systems in general.
Indian Academy of Sciences (India)
start-up company at liT. Mumbai. Part 1. Building Blocks of Quan- tum Computers, Resonance, ..... by modeling the errors caused by decoherence. The interaction of a quantum system with the environment obstructs the unitary evolution of the system and causes dissipation of information, reducing coherence of information.
Indian Academy of Sciences (India)
For the quantum symplectic group S P q ( 2 n ) , we describe the C ∗ -algebra of continuous functions on the quotient space S P q ( 2 n ) / S P q ( 2 n − 2 ) as an universal C ∗ -algebra given by a finite set of generators and relations. The proof involves a careful analysis of the relations, and use of the branching rules for ...
Quantum cryptography beyond quantum key distribution
Broadbent, A.; Schaffner, C.
2016-01-01
Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation,
Quantum cryptography beyond quantum key distribution
A. Broadbent (Anne); C. Schaffner (Christian)
2016-01-01
textabstractQuantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness
Performing quantum computing experiments in the cloud
Devitt, Simon J.
2016-09-01
Quantum computing technology has reached a second renaissance in the past five years. Increased interest from both the private and public sector combined with extraordinary theoretical and experimental progress has solidified this technology as a major advancement in the 21st century. As anticipated my many, some of the first realizations of quantum computing technology has occured over the cloud, with users logging onto dedicated hardware over the classical internet. Recently, IBM has released the Quantum Experience, which allows users to access a five-qubit quantum processor. In this paper we take advantage of this online availability of actual quantum hardware and present four quantum information experiments. We utilize the IBM chip to realize protocols in quantum error correction, quantum arithmetic, quantum graph theory, and fault-tolerant quantum computation by accessing the device remotely through the cloud. While the results are subject to significant noise, the correct results are returned from the chip. This demonstrates the power of experimental groups opening up their technology to a wider audience and will hopefully allow for the next stage of development in quantum information technology.
The Heisenberg representation of quantum computers
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Gottesman, D.
1998-06-24
Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers--the difficulty of describing them on classical computers--also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.
Efficient quantum walk on a quantum processor
Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L.; Wang, Jingbo B.; Matthews, Jonathan C. F.
2016-01-01
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor. PMID:27146471
Efficient quantum walk on a quantum processor.
Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L; Wang, Jingbo B; Matthews, Jonathan C F
2016-05-05
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor.
Orszag, M.; Retamal, J. C.; Saavedra, C.; Wallentowitz, S.
2007-06-01
All the 50 years of conscious pondering did not bring me nearer to an answer to the question `what is light quanta?'. Nowadays, every rascal believes, he knows it, however, he is mistaken. (A Einstein, 1951 in a letter to M Besso) Quantum optics has played a key role in physics in the last several decades. On the other hand, in these early decades of the information age, the flow of information is becoming more and more central to our daily life. Thus, the related fields of quantum information theory as well as Bose-Einstein condensation have acquired tremendous importance in the last couple of decades. In Quantum Optics III, a fusion of these fields appears in a natural way. Quantum Optics III was held in Pucón, Chile, in 27-30 of November, 2006. This beautiful location in the south of Chile is near the lake Villarrica and below the snow covered volcano of the same name. This fantastic environment contributed to a relaxed atmosphere, suitable for informal discussion and for the students to have a chance to meet the key figures in the field. The previous Quantum Optics conferences took place in Santiago, Chile (Quantum Optics I, 2000) and Cozumel, Mexico (Quantum Optics II, 2004). About 115 participants from 19 countries attended and participated in the meeting to discuss a wide variety of topics such as quantum-information processing, experiments related to non-linear optics and squeezing, various aspects of entanglement including its sudden death, correlated twin-photon experiments, light storage, decoherence-free subspaces, Bose-Einstein condensation, discrete Wigner functions and many more. There was a strong Latin-American participation from Argentina, Brazil, Chile, Colombia, Peru, Uruguay, Venezuela and Mexico, as well as from Europe, USA, China, and Australia. New experimental and theoretical results were presented at the conference. In Latin-America a quiet revolution has taken place in the last twenty years. Several groups working in quantum optics and
Theory of interacting quantum fields
Rebenko, Alexei L
2012-01-01
This monograph is devoted to the systematic and encyclopedic presentation of the foundations of quantum field theory. It represents mathematical problems of the quantum field theory with regardto the new methods of the constructive and Euclidean field theory formed for the last thirty years of the 20th century on the basis of rigorous mathematical tools of the functional analysis, the theory of operators, and the theory of generalized functions. The book is useful for young scientists who desire to understand not only the formal structure of the quantum field theory but also its basic concepts and connection with classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of functional integration.
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Goernitz, T.; Weizsaecker, C.F.V.
1987-10-01
Four interpretations of quantum theory are compared: the Copenhagen interpretation (C.I.) with the additional assumption that the quantum description also applies to the mental states of the observer, and three recent ones, by Kochen, Deutsch, and Cramer. Since they interpret the same mathematical structure with the same empirical predictions, it is assumed that they formulate only different linguistic expressions of one identical theory. C.I. as a theory on human knowledge rests on a phenomenological description of time. It can be reconstructed from simple assumptions on predictions. Kochen shows that mathematically every composite system can be split into an object and an observer. Deutsch, with the same decomposition, describes futuric possibilities under the Everett term worlds. Cramer, using four-dimensional action at a distance (Wheeler-Feynman), describes all future events like past facts. All three can be described in the C.I. frame. The role of abstract nonlocality is discussed.
Weber, Timothy
1995-01-01
For extra credit or just for the fun of it-why not try a brainteaser? This collection brings together the first 100 brainteasers from Quantum magazine, published by the National Science Teachers Association in collaboration with the Russian magazine Kvant. Through its pages, you'll find number rebuses, geometry ticklers, logic puzzles, and quirky questions with a physics twist. Students and teachers alike will enjoy these fun quandaries.
Quantum Secure Direct Communication with Quantum Memory.
Zhang, Wei; Ding, Dong-Sheng; Sheng, Yu-Bo; Zhou, Lan; Shi, Bao-Sen; Guo, Guang-Can
2017-06-02
Quantum communication provides an absolute security advantage, and it has been widely developed over the past 30 years. As an important branch of quantum communication, quantum secure direct communication (QSDC) promotes high security and instantaneousness in communication through directly transmitting messages over a quantum channel. The full implementation of a quantum protocol always requires the ability to control the transfer of a message effectively in the time domain; thus, it is essential to combine QSDC with quantum memory to accomplish the communication task. In this Letter, we report the experimental demonstration of QSDC with state-of-the-art atomic quantum memory for the first time in principle. We use the polarization degrees of freedom of photons as the information carrier, and the fidelity of entanglement decoding is verified as approximately 90%. Our work completes a fundamental step toward practical QSDC and demonstrates a potential application for long-distance quantum communication in a quantum network.
Quantum Secure Direct Communication with Quantum Memory
Zhang, Wei; Ding, Dong-Sheng; Sheng, Yu-Bo; Zhou, Lan; Shi, Bao-Sen; Guo, Guang-Can
2017-06-01
Quantum communication provides an absolute security advantage, and it has been widely developed over the past 30 years. As an important branch of quantum communication, quantum secure direct communication (QSDC) promotes high security and instantaneousness in communication through directly transmitting messages over a quantum channel. The full implementation of a quantum protocol always requires the ability to control the transfer of a message effectively in the time domain; thus, it is essential to combine QSDC with quantum memory to accomplish the communication task. In this Letter, we report the experimental demonstration of QSDC with state-of-the-art atomic quantum memory for the first time in principle. We use the polarization degrees of freedom of photons as the information carrier, and the fidelity of entanglement decoding is verified as approximately 90%. Our work completes a fundamental step toward practical QSDC and demonstrates a potential application for long-distance quantum communication in a quantum network.
Experimental quantum forgery of quantum optical money
Bartkiewicz, Karol; Černoch, Antonín; Chimczak, Grzegorz; Lemr, Karel; Miranowicz, Adam; Nori, Franco
2017-03-01
Unknown quantum information cannot be perfectly copied (cloned). This statement is the bedrock of quantum technologies and quantum cryptography, including the seminal scheme of Wiesner's quantum money, which was the first quantum-cryptographic proposal. Surprisingly, to our knowledge, quantum money has not been tested experimentally yet. Here, we experimentally revisit the Wiesner idea, assuming a banknote to be an image encoded in the polarization states of single photons. We demonstrate that it is possible to use quantum states to prepare a banknote that cannot be ideally copied without making the owner aware of only unauthorized actions. We provide the security conditions for quantum money by investigating the physically-achievable limits on the fidelity of 1-to-2 copying of arbitrary sequences of qubits. These results can be applied as a security measure in quantum digital right management.
Information transfer through quantum channels
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Kretschmann, D.
2007-03-12
This PhD thesis represents work done between Aug. 2003 and Dec. 2006 in Reinhard F. Werner's quantum information theory group at Technische Universitaet Braunschweig, and Artur Ekert's Centre for Quantum Computation at the University of Cambridge. My thesis falls into the field of abstract quantum information theory. This work investigates both fundamental properties of quantum channels and their asymptotic capacities for classical as well as quantum information transfer. Stinespring's theorem is the basic structure theorem for quantum channels. It implies that every quantum channel can be represented as a unitary evolution on an enlarged system. In Ch. 3 we present a continuity theorem for Stinespring's representation: two quantum channels are similar if and only if it is possible to find unitary implementations that are likewise similar, with dimension-independent norm bounds. The continuity theorem allows to derive a formulation of the information-disturbance tradeoff in terms of quantum channels, and a continuity estimate for the no-broadcasting principle. In Ch. 4 we then apply the continuity theorem to give a strengthened no-go proof for quantum bit commitment, an important cryptographic primitive. This result also provides a natural characterization of those protocols that fall outside the standard setting of unconditional security, and thus may allow secure bit commitment. We present a new such protocol whose security relies on decoherence in the receiver's lab. Ch. 5 reviews the capacities of quantum channels for the transfer of both classical and quantum information, and investigates several variations in the notion of channel capacity. Memory effects are then investigated in detail in Ch. 6. We advertise a model which is sufficiently general to encompass all causal automata: every quantum process in which the outputs up to any given time t do not depend on the inputs at times t'>t can be represented as a concatenated memory
Modeling of quantum nanomechanics
DEFF Research Database (Denmark)
Jauho, Antti-Pekka; Novotny, Tomas; Donarini, Andrea
2004-01-01
Microelectromechanical systems (MEMS) are approaching the nanoscale, which ultimately implies that the mechanical motion needs to be treated quantum mechanically. In recent years our group has developed theoretical methods to analyze the shuttle transition in the quantum regime (Novotny, 2004......), focusing not only in the IV-curve, but also considering noise, which is an important diagnostic tool in unraveling the microscopic transport mechanisms. Our theoretical analysis is based on a numerical solution of a generalized master equation (GME) for the density matrix. This equation is obtained...... by tracing the Liouville equation over the bath degrees of freedom (i.e., the free fermions of the electronic contacts, and the damping of the mechanical degree of freedom due to a bosonic environment)....
Kleinert, Hagen
2016-01-01
This is an introductory book on elementary particles and their interactions. It starts out with many-body Schrödinger theory and second quantization and leads, via its generalization, to relativistic fields of various spins and to gravity. The text begins with the best known quantum field theory so far, the quantum electrodynamics of photon and electrons (QED). It continues by developing the theory of strong interactions between the elementary constituents of matter (quarks). This is possible due to the property called asymptotic freedom. On the way one has to tackle the problem of removing various infinities by renormalization. The divergent sums of infinitely many diagrams are performed with the renormalization group or by variational perturbation theory (VPT). The latter is an outcome of the Feynman-Kleinert variational approach to path integrals discussed in two earlier books of the author, one representing a comprehensive treatise on path integrals, the other dealing with critial phenomena. Unlike ordin...
Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing
Mazzola, Guglielmo; Smelyanskiy, Vadim N.; Troyer, Matthias
2017-10-01
Quantum tunneling is ubiquitous across different fields, from quantum chemical reactions and magnetic materials to quantum simulators and quantum computers. While simulating the real-time quantum dynamics of tunneling is infeasible for high-dimensional systems, quantum tunneling also shows up in quantum Monte Carlo (QMC) simulations, which aim to simulate quantum statistics with resources growing only polynomially with the system size. Here we extend the recent results obtained for quantum spin models [Phys. Rev. Lett. 117, 180402 (2016), 10.1103/PhysRevLett.117.180402], and we study continuous-variable models for proton transfer reactions. We demonstrate that QMC simulations efficiently recover the scaling of ground-state tunneling rates due to the existence of an instanton path, which always connects the reactant state with the product. We discuss the implications of our results in the context of quantum chemical reactions and quantum annealing, where quantum tunneling is expected to be a valuable resource for solving combinatorial optimization problems.
Working group report: Quantum chromodynamics sub-group
Indian Academy of Sciences (India)
2015-11-27
Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science (IWCCMP-2015). Posted on November 27, 2015. Guest Editors: Anurag Srivastava, C. S. Praveen, H. S. Tewari. © 2017 Indian Academy of Sciences, Bengaluru. Contact | Site index.
Invariant measures on multimode quantum Gaussian states
Energy Technology Data Exchange (ETDEWEB)
Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)
2012-12-15
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Energy Technology Data Exchange (ETDEWEB)
Stapp, Henry
2011-11-10
Robert Griffiths has recently addressed, within the framework of a ‘consistent quantum theory’ (CQT) that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues, on the basis of his examination of certain arguments that claim to demonstrate the existence of such nonlocal influences, that such influences do not exist. However, his examination was restricted mainly to hidden-variable-based arguments that include in their premises some essentially classical-physics-type assumptions that are fundamentally incompatible with the precepts of quantum physics. One cannot logically prove properties of a system by attributing to the system properties alien to that system. Hence Griffiths’ rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his ‘consistent quantum theory’ shows that the cited proof is valid within that restrictive framework. This necessary existence, within the ‘consistent’ framework, of long range essentially instantaneous influences refutes the claim made by Griffiths that his ‘consistent’ framework is superior to the orthodox quantum theory of von Neumann because it does not entail instantaneous influences. An added section responds to Griffiths’ reply, which cites a litany of ambiguities that seem to restrict, devastatingly, the scope of his CQT formalism, apparently to buttress his claim that my use of that formalism to validate the nonlocality theorem is flawed. But the
Pilar, Frank L
2003-01-01
Useful introductory course and reference covers origins of quantum theory, Schrödinger wave equation, quantum mechanics of simple systems, electron spin, quantum states of atoms, Hartree-Fock self-consistent field method, more. 1990 edition.
Energy Technology Data Exchange (ETDEWEB)
Hui, Ning-Ju [Department of Applied Physics, Xi' an University of Technology, Xi' an 710054 (China); Xu, Yang-Yang; Wang, Jicheng; Zhang, Yixin [Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, School of Science, Jiangnan University, Wuxi 214122 (China); Hu, Zheng-Da, E-mail: huyuanda1112@jiangnan.edu.cn [Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, School of Science, Jiangnan University, Wuxi 214122 (China)
2017-04-01
We investigate the properties of geometric quantum coherence in the XY spin-1/2 chain with staggered Dzyaloshinsky-Moriya interaction via the quantum renormalization-group approach. It is shown that the geometric quantum coherence and its coherence susceptibility are effective to detect the quantum phase transition. In the thermodynamic limit, the geometric quantum coherence exhibits a sudden jump. The coherence susceptibilities versus the anisotropy parameter and the Dzyaloshinsky-Moriya interaction are infinite and vanishing, respectively, illustrating the distinct roles of the anisotropy parameter and the Dzyaloshinsky-Moriya interaction in quantum phase transition. Moreover, we also explore the finite-size scaling behaviors of the coherence susceptibilities. For a finite-size chain, the coherence susceptibility versus the phase-transition parameter is always maximal at the critical point, indicating the dramatic quantum fluctuation. Besides, we show that the correlation length can be revealed by the scaling exponent for the coherence susceptibility versus the Dzyaloshinsky-Moriya interaction.
Zhang, Guo-Qing; Xu, Jing-Bo
2017-06-01
We investigate the quantum coherence of an XY spin chain with Dzyaloshinskii-Moriya interaction using a quantum renormalization group-based method, and show that the relative entropy of coherence increases with Dzyaloshinskii-Moriya interaction strength at zero temperature, as well as at finite temperature. We also study the quantum criticality of the system by making use of the relative entropy of coherence and violation of Bell inequality, and find that the first derivatives of the renormalized quantum coherence exhibit singularity near the critical point of the quantum phase transition. Finally, we explore the finite-size scaling behaviors of the derivatives of the quantum coherence at the critical point of the quantum phase transition, and obtain several universal finite-size scaling laws.
Quantum conductance in silicon quantum wires
Bagraev, N T; Klyachkin, L E; Malyarenko, A M; Gehlhoff, W; Ivanov, V K; Shelykh, I A
2002-01-01
The results of investigations of electron and hole quantum conductance staircase in silicon quantum wires are presented. The characteristics of self-ordering quantum wells of n- and p-types, which from on the silicon (100) surface in the nonequilibrium boron diffusion process, are analyzed. The results of investigations of the quantum conductance as the function of temperature, carrier concentration and modulation degree of silicon quantum wires are given. It is found out, that the quantum conductance of the one-dimensional channels is observed, for the first time, at an elevated temperature (T >= 77 K)
Quantum coherence and correlations in quantum system
Xi, Zhengjun; Li, Yongming; Fan, Heng
2015-01-01
Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantum system. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem. PMID:26094795
Quantum correlation with moving beamsplitters in relativistic ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 59; Issue 2. Quantum correlation with moving beamsplitters in ... Zbinden1 Nicolas Gisin1 Antoine Suarez1 2. Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland; Center for Quantum Philosophy, P.O. Box 304, CH-8044 Zurich, Switzerland ...
Hybrid quantum systems: Outsourcing superconducting qubits
Cleland, Andrew
Superconducting qubits offer excellent prospects for manipulating quantum information, with good qubit lifetimes, high fidelity single- and two-qubit gates, and straightforward scalability (admittedly with multi-dimensional interconnect challenges). One interesting route for experimental development is the exploration of hybrid systems, i.e. coupling superconducting qubits to other systems. I will report on our group's efforts to develop approaches that will allow interfacing superconducting qubits in a quantum-coherent fashion to spin defects in solids, to optomechanical devices, and to resonant nanomechanical structures. The longer term goals of these efforts include transferring quantum states between different qubit systems; generating and receiving ``flying'' acoustic phonon-based as well as optical photon-based qubits; and ultimately developing systems that can be used for quantum memory, quantum computation and quantum communication, the last in both the microwave and fiber telecommunications bands. Work is supported by Grants from AFOSR, ARO, DOE and NSF.
On the Classical and Quantum Momentum Map
DEFF Research Database (Denmark)
Esposito, Chiara
In this thesis we study the classical and quantum momentum maps and the theory of reduction. We focus on the notion of momentum map in Poisson geometry and we discuss the classification of the momentum map in this framework. Furthermore, we describe the so-called Poisson Reduction, a technique th...... the quantum action. As an application we discuss some examples of quantum reduction.......In this thesis we study the classical and quantum momentum maps and the theory of reduction. We focus on the notion of momentum map in Poisson geometry and we discuss the classification of the momentum map in this framework. Furthermore, we describe the so-called Poisson Reduction, a technique...... that allows us to reduce the dimension of a manifold in presence of symmetries implemented by Poisson actions. Using techniques of deformation quantization and quantum groups, we introduce the quantum momentum map as a deformation of the classical momentum map, constructed in such a way that it factorizes...
Automata and Quantum Computing
Ambainis, Andris; Yakaryilmaz, Abuzer
2015-01-01
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied. In this paper, we survey various models of quantum finite automata and their properties. We also provide some open questions and new directions for researchers.
Directory of Open Access Journals (Sweden)
Steffen Hahn
2017-01-01
Full Text Available Presently, we are facing a 3σ tension in the most basic cosmological parameter, the Hubble constant H0. This tension arises when fitting the Lambda-cold-dark-matter model (ΛCDM to the high-precision temperature-temperature (TT power spectrum of the Cosmic Microwave Background (CMB and to local cosmological observations. We propose a resolution of this problem by postulating that the thermal photon gas of the CMB obeys an SU(2 rather than U(1 gauge principle, suggesting a high-z cosmological model which is void of dark-matter. Observationally, we rely on precise low-frequency intensity measurements in the CMB spectrum and on a recent model independent (low-z extraction of the relation between the comoving sound horizon rs at the end of the baryon drag epoch and H0 (rsH0=const. We point out that the commonly employed condition for baryon-velocity freeze-out is imprecise, judged by a careful inspection of the formal solution to the associated Euler equation. As a consequence, the above-mentioned 3σ tension actually transforms into a 5σ discrepancy. To make contact with successful low-z ΛCDM cosmology we propose an interpolation based on percolated/depercolated vortices of a Planck-scale axion condensate. For a first consistency test of such an all-z model we compute the angular scale of the sound horizon at photon decoupling.
Fermion-induced quantum critical points.
Li, Zi-Xiang; Jiang, Yi-Fan; Jian, Shao-Kai; Yao, Hong
2017-08-22
A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.
Preface of the special issue quantum foundations: information approach.
D'Ariano, Giacomo Mauro; Khrennikov, Andrei
2016-05-28
This special issue is based on the contributions of a group of top experts in quantum foundations and quantum information and probability. It enlightens a number of interpretational, mathematical and experimental problems of quantum theory. © 2016 The Author(s).
Quantum gravity and quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Inst. de Estructura de la Materia; Papantonopoulos, Lefteris [National Technical Univ. of Athens (Greece). Dept. of Physics; Siopsis, George [Tennessee Univ., Knoxville, TN (United States). Dept. of Physics and Astronomy; Tsamis, Nikos (eds.) [Crete Univ, Heraklion (Greece). Dept. of Physics
2013-02-01
With contributions by leading researcher in the field. Chapters written as both tutorial and state-of-the-art surveys. Can be used both as advanced course material and for self study. Quantum gravity has developed into a fast-growing subject in physics and it is expected that probing the high-energy and high-curvature regimes of gravitating systems will shed some light on how to eventually achieve an ultraviolet complete quantum theory of gravity. Such a theory would provide the much needed information about fundamental problems of classical gravity, such as the initial big-bang singularity, the cosmological constant problem, Planck scale physics and the early-time inflationary evolution of our Universe. While in the first part of this book concepts of quantum gravity are introduced and approached from different angles, the second part discusses these theories in connection with cosmological models and observations, thereby exploring which types of signatures of modern and mathematically rigorous frameworks can be detected by experiments. The third and final part briefly reviews the observational status of dark matter and dark energy, and introduces alternative cosmological models.
Quantum Correlations Evolution Asymmetry in Quantum Channels
Li, Meng; Huang, Yun-Feng; Guo, Guang-Can
2017-03-01
It was demonstrated that the entanglement evolution of a specially designed quantum state in the bistochastic channel is asymmetric. In this work, we generalize the study of the quantum correlations, including entanglement and quantum discord, evolution asymmetry to various quantum channels. We found that the asymmetry of entanglement and quantum discord only occurs in some special quantum channels, and the behavior of the entanglement evolution may be quite different from the behavior of the quantum discord evolution. To quantum entanglement, in some channels it decreases monotonously with the increase of the quantum channel intensity. In some other channels, when we increase the intensity of the quantum channel, it decreases at first, then keeps zero for some time, and then rises up. To quantum discord, the evolution becomes more complex and you may find that it evolutes unsmoothly at some points. These results illustrate the strong dependence of the quantum correlations evolution on the property of the quantum channels. Supported by the National Natural Science Foundation of China under Grant Nos. 61327901, 61490711, 61225025, 11474268, and the Fundamental Research Funds for the Central Universities under Grant No. WK2470000018
Schürmann, Michael
2008-01-01
This volume contains the revised and completed notes of lectures given at the school "Quantum Potential Theory: Structure and Applications to Physics," held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald from February 26 to March 10, 2007. Quantum potential theory studies noncommutative (or quantum) analogs of classical potential theory. These lectures provide an introduction to this theory, concentrating on probabilistic potential theory and it quantum analogs, i.e. quantum Markov processes and semigroups, quantum random walks, Dirichlet forms on C* and von Neumann algebras, and boundary theory. Applications to quantum physics, in particular the filtering problem in quantum optics, are also presented.
Quantum information processing in nanostructures Quantum optics; Quantum computing
Reina-Estupinan, J H
2002-01-01
Since information has been regarded os a physical entity, the field of quantum information theory has blossomed. This brings novel applications, such as quantum computation. This field has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineering, to the physical sciences. Thus, we now have an interdisciplinary field where great efforts are being made in order to build devices that should allow for the processing of information at a quantum level, and also in the understanding of the complex structure of some physical processes at a more basic level. This thesis is devoted to the theoretical study of structures at the nanometer-scale, 'nanostructures', through physical processes that mainly involve the solid-state and quantum optics, in order to propose reliable schemes for the processing of quantum information. Initially, the main results of quantum information theory and quantum computation are briefly reviewed. Next, the state-of-the-art of ...
1990-01-01
Quantum electrodynamics is an essential building block and an integral part of the gauge theory of unified electromagnetic, weak, and strong interactions, the so-called standard model. Its failure or breakdown at some level would have a most profound impact on the theoretical foundations of elementary particle physics as a whole. Thus the validity of QED has been the subject of intense experimental tests over more than 40 years of its history. This volume presents an up-to-date review of high precision experimental tests of QED together with comprehensive discussion of required theoretical wor
Jitrik, Oliverio; Lanzagorta, Marco; Uhlmann, Jeffrey; Venegas-Andraca, Salvador E.
2017-05-01
The study of plate tectonic motion is important to generate theoretical models of the structure and dynamics of the Earth. In turn, understanding tectonic motion provides insight to develop sophisticated models that can be used for earthquake early warning systems and for nuclear forensics. Tectonic geodesy uses the position of a network of points on the surface of earth to determine the motion of tectonic plates and the deformation of the earths crust. GPS and interferometric synthetic aperture radar are commonly used techniques used in tectonic geodesy. In this paper we will describe the feasibility of interferometric synthetic aperture quantum radar and its theoretical performance for tectonic geodesy.
Neubert, Matthias
1996-01-01
Quantum chromodynamics (QCD) is the fundamental theory of the strong interactions. It is local, non-abelian gauge theory descripting the interactions between quarks and gluons, the constituents of hadrons. In these lectures, the basic concepts and ph will be introduced in a pedagogical way. Topics will include : asymptotically free partons, colour and confinement ; non-abelian gauge invariance and quantization ; the running coupling constant ; deep-inelastic scattering and scaling violations ; th chiral and heavy-quark symmetries. Some elementary knowledge of field theory, abelian gauge invariance and Feynman diagrams will be helpful in following the course.
Mandl, Franz
1992-01-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scient
Kawahara, Miho; Nemoto, Maki; Nakata, Toru; Kondo, Saya; Takahashi, Hajime; Kimura, Bon; Kuda, Takashi
2015-06-01
Six lactic acid bacteria strains (four Lactobacillus plantarum strains and one each of Lactococcus lactis subsp. lactis and Pediococcus pentosaceus) have been isolated and shown to possess anti-oxidant activity. In this study, we determined their acid, bile, salt resistance, and adhesion activity on human enterocyte-like HT-29-Luc and Caco-2 cells. An isolate Lc. lactis S-SU2 showed highest bile resistance and adhesion activity compared to type strains. S-SU2 could ferment both 10% skimmed milk and soy milk while the type strain could not ferment soy milk. Soy milk fermented with S-SU2 showed an increased nitric oxide (NO) secretion in the mouse macrophage RAW264.7 cells without bacterial lipopolysaccharide (LPS). Furthermore, the inhibitory effects of the fermented soy milk on Escherichia coli O111 LPS-induced NO secretion were higher than those of fresh soy milk. Inflammatory bowel disease (IBD) was induced in mice fed either 5% (w/v) dextran sodium sulfate (DSS) in drinking water or 50% soy milk in drinking water. Shortening of colon length, breaking of epithelial cells, lowering liver and thymus weights, and enlargement of spleen are some of the characteristics observed in the IBD, which were prevented by the use of soy milk fermented with Lc. lactis S-SU2. Copyright © 2015 Elsevier B.V. All rights reserved.
Digestible quantum field theory
Smilga, Andrei
2017-01-01
This book gives an intermediate level treatment of quantum field theory, appropriate to a reader with a first degree in physics and a working knowledge of special relativity and quantum mechanics. It aims to give the reader some understanding of what QFT is all about, without delving deep into actual calculations of Feynman diagrams or similar. The author serves up a seven‐course menu, which begins with a brief introductory Aperitif. This is followed by the Hors d'oeuvres, which set the scene with a broad survey of the Universe, its theoretical description, and how the ideas of QFT developed during the last century. In the next course, the Art of Cooking, the author recaps on some basic facts of analytical mechanics, relativity, quantum mechanics and also presents some nutritious “extras” in mathematics (group theory at the elementary level) and in physics (theory of scattering). After these preparations, the reader should have a good appetite for the Entrées ‐ the central par t of the book where the...
Quantum Cybernetics and Complex Quantum Systems Science - A Quantum Connectionist Exploration
Gonçalves, Carlos Pedro
2014-01-01
Quantum cybernetics and its connections to complex quantum systems science is addressed from the perspective of complex quantum computing systems. In this way, the notion of an autonomous quantum computing system is introduced in regards to quantum artificial intelligence, and applied to quantum artificial neural networks, considered as autonomous quantum computing systems, which leads to a quantum connectionist framework within quantum cybernetics for complex quantum computing systems. Sever...
Quantum entanglement and quantum computational algorithms
Indian Academy of Sciences (India)
Abstract. The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We demonstrate that the one- and the two-bit Deutsch-Jozsa algorithm does not require entanglement and can be mapped ...
The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory
Frey, Kimberly
The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum
Controlled Alternate Quantum Walks based Quantum Hash Function.
Li, Dan; Yang, Yu-Guang; Bi, Jing-Lin; Yuan, Jia-Bin; Xu, Juan
2018-01-09
Through introducing controlled alternate quantum walks, we present controlled alternate quantum walks (CAQW) based quantum hash function. CAQW based quantum hash function have excellent security, outstanding statistical performance and splendid expansibility. Furthermore, due to the structure of alternate quantum walks, implementing CAQW based quantum hash function significantly reduces the resources necessary for its feasible experimental realization than implementing other quantum hash functions.
Rebuilding mathematics on a quantum logical foundation
DeJonghe, Richard J., III
We construct a rich first-order quantum logic which generalizes the standard classical predicate logic used in the development of virtually all of modern mathematics, and we use this quantum logic to build the foundations of a new quantum mathematics. First, we prove both soundness and completeness for the quantum logic we develop, and also prove a powerful new completeness result which heretofore had been known to hold for classical, but not quantum, first-order logic. We then use our quantum logic to develop multiple areas of mathematics, including abstract algebra, axiomatic set theory, and arithmetic. In some preliminary investigations into quantum mathematics, Dunn found that the Peano axioms for arithmetic yield the same theorems using either classical or quantum logic. We prove a similar result for certain classes of abstract algebras, and then show that Dunn's result is not generic by presenting examples of quantum monoids, groups, lattices, vector spaces, and operator algebras, all which differ from their classical counterparts. Moreover, we find natural classes of quantum lattices, vector spaces, and operator algebras which all have a beautiful inter-relationship, and make some preliminary investigations into using these structures as a basis for a new mathematical formulation of quantum mechanics. We also develop a quantum set theory (equivalent to ZFC under classical logic) which is far more tractable than quantum set theory previously developed. We then use this set theory to construct a quantum version of the natural numbers, and develop an arithmetic of these numbers based upon an alternative to Peano's axioms (which avoids Dunn's theorem). Surprisingly, we find that these "quantum natural numbers" satisfy our arithmetical axioms if and only if the underlying truth values form a modular lattice, giving a new arithmetical characterization of this important lattice-theoretic property. Finally, we show that these numbers have a natural interpretation as
De Raedt, H. A.; Hams, A. H.; Michielsen, K. F. L.; De Raedt, K.
2000-01-01
We describe a quantum computer emulator for a generic, general purpose quantum computer. This emulator consists of a simulator of the physical realization of the quantum computer and a graphical user interface to program and control the simulator. We illustrate the use of the quantum computer emulator through various implementations of the Deutsch-Jozsa and Grover's database search algorithm.
Quantum Entanglement and Teleportation
Yates, Brent R.
2011-01-01
Even Einstein has to be wrong sometimes. However, when Einstein was wrong he created a 70 year debate about the strange behavior of quantum mechanics. His debate helped prove topics such as the indeterminacy of particle states, quantum entanglement, and a rather clever use of quantum entanglement known as quantum teleportation.
On Quantum Microcanonical Equilibrium
Dorje C. Brody; Hook, Daniel W.; Hughston, Lane P.
2007-01-01
A quantum microcanonical postulate is proposed as a basis for the equilibrium properties of small quantum systems. Expressions for the corresponding density of states are derived, and are used to establish the existence of phase transitions for finite quantum systems. A grand microcanonical ensemble is introduced, which can be used to obtain new rigorous results in quantum statistical mechanics. Accepted version
On quantum microcanonical equilibrium
Energy Technology Data Exchange (ETDEWEB)
Brody, Dorje C [Department of Mathematics, Imperial College, London SW7 2BZ (United Kingdom); Hook, Daniel W [Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom); Hughston, Lane P [Department of Mathematics, King' s College London, The Strand, London WC2R 2LS (United Kingdom)
2007-05-15
A quantum microcanonical postulate is proposed as a basis for the equilibrium properties of small quantum systems. Expressions for the corresponding density of states are derived, and are used to establish the existence of phase transitions for finite quantum systems. A grand microcanonical ensemble is introduced, which can be used to obtain new rigorous results in quantum statistical mechanics.
Quantum Closures and Disclosures
African Journals Online (AJOL)
denise
thought that a living, quantum dynamically functioning brain is a unique locus where both the existence of a world and our experience of it are created. Globus takes from QBD the idea that there are two quantum universes, both of them unpresent. One of these is the quantum universe familiar from quantum mechanics (“our” ...
Calmet, Xavier; Winstanley, Elizabeth
2014-01-01
Written by foremost experts, this short book gives a clear description of the physics of quantum black holes. The reader will learn about quantum black holes in four and higher dimensions, primordial black holes, the production of black holes in high energy particle collisions, Hawking radiation, black holes in models of low scale quantum gravity and quantum gravitational aspects of black holes.
Garcia-Escartin, Juan Carlos; Chamorro-Posada, Pedro
2011-01-01
Quantum algorithms and protocols are often presented as quantum circuits for a better understanding. We give a list of equivalence rules which can help in the analysis and design of quantum circuits. As example applications we study quantum teleportation and dense coding protocols in terms of a simple XOR swapping circuit and give an intuitive picture of a basic gate teleportation circuit.
Quantum Metrology: Surpassing the shot-noise limit with Dzyaloshinskii-Moriya interaction.
Ozaydin, Fatih; Altintas, Azmi Ali
2015-11-09
Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. However the effects on the entanglement dynamics such as decoherence usually decrease the QFI considerably. On the other hand, Dzyaloshinskii-Moriya (DM) interaction has been shown to excite entanglement. Since an increase in entanglement does not imply an increase in QFI, and also there are cases where QFI decreases as entanglement increases, it is interesting to study the influence of DM interaction on quantum metrology. In this work, we study the QFI of thermal entanglement of two-qubit and three-qubit Heisenberg models with respect to SU(2) rotations. We show that even at high temperatures, DM interaction excites QFI of both ferromagnetic and antiferromagnetic models. We also show that QFI of the ferromagnetic model of two qubits can surpass the shot-noise limit of the separable states, while QFI of the antiferromagnetic model in consideration can only approach to the shot-noise limit. Our results open new insights in quantum metrology with Heisenberg models.