Homomorphisms of quantum groups
Meyer, Ralf; Woronowicz, Stanisław Lech
2010-01-01
We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions, and universal quantum groups, respectively.
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...
Applications of Quantum Groups
Chryssomalakos, Chryssomalis
The main theme of this thesis is the search for applications of Quantum Group and Hopf algebraic concepts and techniques in Physics. We investigate in particular the possibilities that exist in deforming, in a self consistent way, the symmetry structure of physical theories with the hope that the resulting scheme will be of relevance in the description of physical reality. Our choice of topics reflects this motivation: we discuss deformations of rotations and Lorentz boosts, search for integrals on the quantum plane and attempt to Fourier transform functions of non -commuting coordinates. Along the way, more formal considerations prompt us to revisit integration on finite dimensional Hopf algebras, explore the interconnections between various descriptions of the quantum double and derive the algebraic structure of the quantum plane from that of the underlying deformed symmetry group. The material is structured as follows. Chapter 1 introduces the language, basic concepts and notation employed throughout this thesis. Chapter 2 focuses on Hopf algebras viewed as universal envelopes of deformed Lie algebras and their duals. Bicovariant generators enter the discussion as analogues of the classical Lie algebra generators and some of their properties are given. We comment on the geometrical interpretation of the algebraic formulation and introduce computational tools. In chapter 3 we take a close look at the quantum Lorentz Hopf algebra. The basics of complex quantum groups are presented and applied in the derivation of the algebra of the quantum Lorentz generators and its Hopf and involutive structures. We point also to isomorphisms with previous related constructions. The subject of quantum integration is explored in chapter 4. We derive a formula for the integral on a finite dimensional Hopf algebra and show its equivalence to the formulation in terms of the trace of the square of the antipode. Integration on the quantum plane is also examined and a Fourier transform
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).
Quantum threshold group signature
Institute of Scientific and Technical Information of China (English)
2008-01-01
In most situations, the signer is generally a single person. However, when the message is written on behalf of an organization, a valid message may require the approval or consent of several persons. Threshold signature is a solution to this problem. Generally speaking, as an authority which can be trusted by all members does not exist, a threshold signature scheme without a trusted party appears more attractive. Following some ideas of the classical Shamir’s threshold signature scheme, a quantum threshold group signature one is proposed. In the proposed scheme, only t or more of n persons in the group can generate the group signature and any t-1 or fewer ones cannot do that. In the verification phase, any t or more of n signature receivers can verify the message and any t-1 or fewer receivers cannot verify the validity of the signature.
Quantum groups: Geometry and applications
Energy Technology Data Exchange (ETDEWEB)
Chu, C.S. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group
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.
DEFF Research Database (Denmark)
2015-01-01
We study the BGG-categories O_q associated to quantum groups. We prove that many properties of the ordinary BGG-category O for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when q is a complex root of unity. Here we prove a tensor decomposition...
Bicrossproducts of algebraic quantum groups
Delvaux, Lydia; Wang, Shuanhong
2012-01-01
Let $A$ and $B$ be two algebraic quantum groups (i.e. multiplier Hopf algebras with integrals). Assume that $B$ is a right $A$-module algebra and that $A$ is a left $B$-comodule coalgebra. If the action and coaction are matched, it is possible to define a coproduct $\\Delta_#$ on the smash product $A # B$ making the pair $(A # B,\\Delta_#)$ into an algebraic quantum group. In this paper, we continue the study of these objects. First, we study the various data of the bicrossproduct $A # B$, such as the modular automorphisms, the modular elements, ... and obtain formulas in terms of the data of the components $A$ and $B$. Secondly, we look at the dual of $A # B$ (in the sense of algebraic quantum groups) and we show it is itself a bicrossproduct (of the second type) of the duals $\\hatA$ and $\\hatB$. The result is immediate for finite-dimensional Hopf algebras and therefore it is expected also for algebraic quantum groups. However, it turns out that some aspects involve a careful argument, mainly due to the fact t...
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...
Representation Theory of Algebraic Groups and Quantum Groups
Gyoja, A; Shinoda, K-I; Shoji, T; Tanisaki, Toshiyuki
2010-01-01
Invited articles by top notch expertsFocus is on topics in representation theory of algebraic groups and quantum groupsOf interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics
Fusion Rings for Quantum Groups
DEFF Research Database (Denmark)
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....
Fusion Rings for Quantum Groups
DEFF Research Database (Denmark)
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....
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....
Quantum group blind signature scheme without entanglement
Xu, Rui; Huang, Liusheng; Yang, Wei; He, Libao
2011-07-01
In this paper we propose a quantum group blind signature scheme designed for distributed e-voting system. Our scheme combines the properties of group signature and blind signature to provide anonymity of voters in an e-voting system. The unconditional security of our scheme is ensured by quantum mechanics. Without employing entanglement, the proposed scheme is easier to be realized comparing with other quantum signature schemes.
Applications of Foelner's condition to quantum groups
Kyed, David
2009-01-01
Using the Foelner condition for coamenable quantum groups we derive information about the ring theoretical structure of the Hopf algebras arising from such quantum groups, as well as an approximation result concerning the Murray von Neumann dimension associated with the corresponding the von Neumann algebra.
Quantum groups, deformed oscillators and their interrelations
Damaskinsky, E V; Damaskinsky, E V; Kulish, P P
1995-01-01
The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: GL_q(2), sl_q(2), q-oscillator algebra {\\cal A}(q), and reflection equation algebra. The Gauss decompositions of quantum groups and their realizations in terms of\\, {\\cal A}(q) are given.
From knots to quantum groups (and back)
Energy Technology Data Exchange (ETDEWEB)
Kauffman, L. (Illinois Univ., Chicago, IL (USA) Argonne National Lab., IL (USA))
1990-04-01
This paper traces how the Jones polynomial leads naturally to the notion of quantum group, and how quantum groups give rise to invariants of links via solutions to the Yang-Baxter equation. Section 5, is an original treatment of the construction of the universal R-matrix. All the other material has, or will appear elsewhere in similar form.
Universal C*-algebraic quantum groups arising from algebraic quantum groups
Kustermans, J
1997-01-01
In this paper, we construct a universal C*-algebraic quantum group out of an algebraic one. We show that this universal C*-algebraic quantum group has the same rich structure as its reduced companion. This universal C*-algebraic quantum group also satifies an upcoming definition of Masuda, Nakagami & Woronowicz except for the possible non-faithfulness of the left Haar weight.
The cluster variety face of quantum groups
Popolitov, Alexandr
2014-01-01
Using the well-known free-field formalism for quantum groups, we demonstrate in case of $A(n)_q$, that quantum group is naturally also a cluster variety. Widely used formulae for mutations are direct consequence of independence of group element on the order of simple roots. Usual formulae for $2 n$ Poisson leaf emerge in classical limit, if all but few ($2n$) coordinates vanish.
The analytic structure of an algebraic quantum group
Kustermans, J
1997-01-01
A. Van Daele introduced and investigated so-called algebraic quantum groups. We proved that such algebraic quantum groups give rise to C*-algebraic quantum groups in the sense of Masuda, Nakagami & Woronowicz. We prove in this paper that the analytic structure of these C*-algebraic quantum groups can be pulled down to the algebraic quantum group.
Property (T) and exotic quantum group norms
Kyed, David
2010-01-01
Utilizing the notion of property (T) we construct new examples of quantum group norms on the polynomial algebra of a compact quantum group, and provide criteria ensuring that these are not equal to neither the minimal nor the maximal norm. Along the way we generalize several classical operator algebraic characterizations of property (T) to the quantum group setting which unify recent approaches to property (T) for quantum groups with previous ones. The techniques developed furthermore provide tools to answer two open problems; firstly a question by B\\'edos, Murphy and Tuset about automatic continuity of the comultiplication and secondly a problem left open by Woronowicz regarding the structure of elements whose coproduct is a finite sum of simple tensors.
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.
De Finetti theorems for easy quantum groups
Banica, Teodor; Speicher, Roland
2009-01-01
We study sequences of noncommutative random variables which are invariant under "quantum transformations" coming from an orthogonal quantum group satisfying the "easiness" condition axiomatized in our previous paper. For 10 easy quantum groups, we obtain de Finetti type theorems characterizing the joint distribution of any infinite, quantum invariant sequence. In particular, we give a new and unified proof of the classical results of de Finetti and Freedman for the easy groups S_n, O_n, which is based on the combinatorial theory of cumulants. We also recover the free de Finetti theorem of K\\"ostler and Speicher, and the characterization of operator-valued free semicircular families due to Curran. We consider also finite sequences, and prove an approximation result in the spirit of Diaconis and Freedman.
Poisson boundaries over locally compact quantum groups
Kalantar, Mehrdad; Ruan, Zhong-Jin
2011-01-01
We present versions of several classical results on harmonic functions and Poisson boundaries in the setting of locally compact quantum groups $\\mathbb{G}$. In particular, the Choquet-Deny theorem holds for compact quantum groups; also, the result of Kaimanovich-Vershik and Rosenblatt, which characterizes group amenability in terms of harmonic functions, answering a conjecture by Furstenberg, admits a non-commutative analogue in the separable case. We also explore the relation between classical and quantum Poisson boundaries by investigating the spectrum of the quantum group. We apply this machinery to find a concrete realization of the Poisson boundaries of the compact quantum group $SU_{q}(2)$ arising from measures on its spectrum. We further show that the Poisson boundary of the natural Markov operator extension of the convolution action of a quantum probability measure $\\mu$ on $L_\\infty(\\mathbb{G})$ to $B(L_2(\\mathbb{G}))$, as introduced and studied - for general completely bounded multipliers on $L_1(\\m...
Quasi-quantum groups from strings
Jureit, J -H
2007-01-01
Motivated by string theory on the orbifold ${\\cal M}/G$ in presence of a Kalb-Ramond field strength $H$, we define the operators that lift the group action to the twisted sectors. These operators turn out to generate the quasi-quantum group $D_{\\omega}[G]$, introduced in the context of conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche, with $\\omega$ a 3-cocycle determined by a series of cohomological equations in a tricomplex combining de Rham, \\u{C}ech and group cohomologies. We further illustrate some properties of the quasi-quantum group from a string theoretical point of view.
Working group report: Quantum chromodynamics
Indian Academy of Sciences (India)
V Ravindra; Pankaj Agrawal; Rahul Basu; Satyaki Bhattacharya; J Blümlein; V Del Duca; R Harlander; D Kosower; Prakash Mathews; Anurag Tripathi
2006-11-01
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.
On the geometry of inhomogeneous quantum groups
Energy Technology Data Exchange (ETDEWEB)
Aschieri, Paolo [Scuola Normale Superiore, Pisa (Italy)
1998-01-01
The author gives a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case. He further analyzes the relation between differential calculus and quantum Lie algebra of left (right) invariant vectorfields. Equivalent definitions of bicovariant differential calculus are studied and their geometrical interpretation is explained. From these data he constructs and analyzes the space of vectorfields, and naturally introduces a contraction operator and a Lie derivative. Their properties are discussed.
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.
Lacunary Fourier Series for Compact Quantum Groups
Wang, Simeng
2016-05-01
This paper is devoted to the study of Sidon sets, {Λ(p)} -sets and some related notions for compact quantum groups. We establish several different characterizations of Sidon sets, and in particular prove that any Sidon set in a discrete group is a strong Sidon set in the sense of Picardello. We give several relations between Sidon sets, {Λ(p)} -sets and lacunarities for L p -Fourier multipliers, generalizing a previous work by Blendek and Michalic̆ek. We also prove the existence of {Λ(p)} -sets for orthogonal systems in noncommutative L p -spaces, and deduce the corresponding properties for compact quantum groups. Central Sidon sets are also discussed, and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central Sidon sets. Several examples are also included.
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.
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.
The small quantum group as a quantum double
Etingof, Pavel; Gelaki, Shlomo
2009-01-01
We prove that the quantum double of the quasi-Hopf algebra A_q(g) of dimension n^{dim g} attached in arXiv:math/0403096 to a simple complex Lie algebra g and a primitive root of unity q of order n^2 is equivalent to Lusztig's small quantum group u_q(g) (under some conditions on n). We also give a conceptual construction of A_q(g) using the notion of de-equivariantization of tensor categories.
Gauss decomposition for quantum groups and duality
Damaskinsky, E V; Lyakhovsky, V D; Sokolov, M A
1995-01-01
The Gauss decomposition of quantum groups and supergroups are considered. The main attention is paid to the R-matrix formulation of the Gauss decomposition and its properties as well as its relation to the contraction procedure. Duality aspects of the Gauss decomposition are also touched. For clarity of exposition a few simple examples are considered in some details.
Quasi-quantum groups from strings
Energy Technology Data Exchange (ETDEWEB)
Jureit, J-H; Krajewski, T [Centre de Physique Theorique, Campus de Luminy, 13288 Marseille (France)], E-mail: jureit@cpt.univ-mrs.fr, E-mail: krajew@cpt.univ-mrs.fr
2008-02-01
Motivated by string theory on the orbifold M/G in presence of a Kalb-Ramond field strength H, we define the operators that lift the group action to the twisted sectors. These operators turn out to generate the quasi-quantum group D{sub {omega}}[G], introduced in the context of conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche, with {omega} a 3-cocycle determined by a series of cohomological equations in a tricomplex combining de Rham, Cech and group cohomologies. We further illustrate some properties of the quasi-quantum group from a string theoretical point of view. This work is based on [2], from which a full-fledged treatment may be extracted.
Cyclic groups and quantum logic gates
Pourkia, Arash; Batle, J.; Raymond Ooi, C. H.
2016-10-01
We present a formula for an infinite number of universal quantum logic gates, which are 4 by 4 unitary solutions to the Yang-Baxter (Y-B) equation. We obtain this family from a certain representation of the cyclic group of order n. We then show that this discrete family, parametrized by integers n, is in fact, a small sub-class of a larger continuous family, parametrized by real numbers θ, of universal quantum gates. We discuss the corresponding Yang-Baxterization and related symmetries in the concomitant Hamiltonian.
Topological Quantum Hashing with the Icosahedral Group
Burrello, Michele; Xu, Haitan; Mussardo, Giuseppe; Wan, Xin
2010-04-01
We study an efficient algorithm to hash any single-qubit gate into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudogroups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O(log2(1/ɛ)), we can approximate all SU(2) matrices to an average error ɛ with a cost of O(log(1/ɛ)) in time. The algorithm is applicable to generic quantum compiling.
Group representations, error bases and quantum codes
Energy Technology Data Exchange (ETDEWEB)
Knill, E
1996-01-01
This report continues the discussion of unitary error bases and quantum codes. Nice error bases are characterized in terms of the existence of certain characters in a group. A general construction for error bases which are non-abelian over the center is given. The method for obtaining codes due to Calderbank et al. is generalized and expressed purely in representation theoretic terms. The significance of the inertia subgroup both for constructing codes and obtaining the set of transversally implementable operations is demonstrated.
Schr\\"odinger group and quantum finance
Romero, Juan M; Martínez, Elio
2013-01-01
Using the one dimensional free particle symmetries, the quantum finance symmetries are obtained. Namely, it is shown that Black-Scholes equation is invariant under Schr\\"odinger group. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited. To get the Black-Scholes equation symmetries, the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schr\\"odinger algebra representation is constructed.
A Delorme-Guichardet Theorem for quantum groups
Kyed, David
2010-01-01
We prove a Delorme-Guichardet Theorem for discrete quantum groups, expressing property (T) of a quantum group in terms of vanishing of its first cohomology groups. As an application, we show that the first L^2-Betti number of a discrete property (T) quantum group vanishes.
A group signature scheme based on quantum teleportation
Energy Technology Data Exchange (ETDEWEB)
Wen Xiaojun; Tian Yuan; Ji Liping; Niu Xiamu, E-mail: wxjun36@gmail.co [Information Countermeasure Technique Research Institute, Harbin Institute of Technology, Harbin 150001 (China)
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.
Quantum isometry groups of noncommutative manifolds associated to group C*-algebras
Bhowmick, Jyotishman
2010-01-01
Let G be a finitely generated discrete group. The standard spectral triple on the group C*-algebra C*(G) is shown to admit the quantum group of orientation preserving isometries. This leads to new examples of compact quantum groups. In particular the quantum isometry group of the C*-algebra of the free group on n-generators is computed and shown to be a quantum group extension of the quantum permutation group A_{2n} of Wang. The quantum groups of orientation and real structure preserving isometries are also considered and construction of the Laplacian for the standard spectral triple on C*(G) discussed.
Quantum isometry groups of noncommutative manifolds associated to group C∗-algebras
Bhowmick, Jyotishman; Skalski, Adam
2010-10-01
Let Γ be a finitely generated discrete group. The standard spectral triple on the group C∗-algebra C∗(Γ) is shown to admit the quantum group of orientation preserving isometries. This leads to new examples of compact quantum groups. In particular, the quantum isometry group of the C∗-algebra of the free group on n generators is computed and turns out to be a quantum group extension of the quantum permutation group A2n of Wang. The quantum groups of orientation and real structure preserving isometries are also considered and the construction of the Laplacian for the standard spectral triple on C∗(Γ) is discussed.
Geometry of Quantum Group Twists, Multidimensional Jackson Calculus and Regularization
Demichev, A. P.
1995-01-01
We show that R-matricies of all simple quantum groups have the properties which permit to present quantum group twists as transitions to other coordinate frames on quantum spaces. This implies physical equivalence of field theories invariant with respect to q-groups (considered as q-deformed space-time groups of transformations) connected with each other by the twists. Taking into account this freedom we study quantum spaces of the special type: with commuting coordinates but with q-deformed ...
Affinization of category O for quantum groups
Young, C A S
2012-01-01
Let g be a simple Lie algebra. We consider the category O-hat of those modules over the affine quantum group Uq(g-hat) whose Uq(g)-weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that many properties of the category of the finite-dimensional representations naturally extend to the category O-hat. In particular, we develop the theory of q-characters and define the minimal affinizations of parabolic Verma modules. In types ABCFG we classify these minimal affinizations and conjecture a Weyl denominator type formula for their characters.
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...
Group Field Theory and Loop Quantum Gravity
Oriti, Daniele
The following sections are included: * GFT from LQG Perspective: The Underlying Ideas * GFT Kinematics: Hilbert Space and Observables * The Quantum Dynamics * The Continuum Limit of Quantum Geometry in GFT * Extracting Effective Continuum Physics from GFTs * Conclusions * References
Quantum groups and quantum field theory III. Renormalisation
Brouder, C; Brouder, Christian; Schmitt, William
2002-01-01
The Hopf algebra of renormalisation in quantum field theory is described at a general level. The products of fields at a point are assumed to form a bialgebra B and renormalisation endows T(T(B)^+), the double tensor algebra of B, with the structure of a noncommutative bialgebra. When the bialgebra B is commutative, renormalisation turns S(S(B)^+), the double symmetric algebra of B, into a commutative bialgebra. The usual Hopf algebra of renormalisation is recovered when the elements of $T^1(B)$ are not renormalised, i.e. when Feynman diagrams containing one single vertex are not renormalised. When B is the Hopf algebra of a commutative group, a homomorphism is established between the bialgebra S(S(B)^+) and the Faa di Bruno bialgebra of composition of series. The relation with the Connes-Moscovici Hopf algebra of diffeomorphisms is given. Finally, the bialgebra S(S(B)^+) is shown to give the same results as the standard renormalisation procedure for the scalar field.
Isometric Coactions of Compact Quantum Groups on Compact Quantum Metric Spaces
Indian Academy of Sciences (India)
Johan Quaegebeur; Marie Sabbe
2012-08-01
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.
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.
Topological quantum groups, star products and their relations
Flato, M; Flato, M; Sternheimer, D
1994-01-01
This short summary of recent developments in quantum compact groups and star products is divided into 2 parts. In the first one we recast star products in a more abstract form as deformations and review its recent developments. The second part starts with a rapid presentation of standard quantum group theory and its problems, then moves to their completion by introduction of suitable Montel topologies well adapted to duality. Preferred deformations (by star products and unchanged coproducts) of Hopf algebras of functions on compact groups and their duals, are of special interest. Connection with the usual models of quantum groups and the quantum double is then presented.
Krovi, Hari; Russell, Alexander
2012-01-01
Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finite-dimensional Hopf algebras: quantum doubles of finite groups (denoted D(G), for a group G). Regarding algorithms for these invariants, we develop quantum circuits for the quantum Fourier transform over D(G); in general, we show that when one can uniformly and efficiently carry out the quantum Fourier transform over the ce...
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.)
Coherent States, Dynamics and Semiclassical Limit on Quantum Groups
Aref'eva, I Ya; Viswanathan, K S; Volovich, I V
1994-01-01
Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit $q\\rightarrow 1$ is discussed and the crucial role of special states on the quantum algebra in an investigation of the semiclassical limit is emphasized. An approach to $q$-deformation as a $q$-Weyl quantization and a relavence of contact geometry in this context is pointed out. Dynamics on the quantum group parametrized by a real time variable and corresponding to classical rotations is considered.
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.
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 many of the existing schemes completely break down once quantum computers reach maturity (mainly due to Shor's algorithm). This leads to the challenge of constructing quantum-resistant group homom...
The Baum-Connes conjecture for free orthogonal quantum groups
Voigt, Christian
2009-01-01
We prove an analogue of the Baum-Connes conjecture for free orthogonal quantum groups. More precisely, we show that these quantum groups have a $ \\gamma $-element and that $ \\gamma = 1 $. It follows that free orthogonal quantum groups are $ K $-amenable. We compute explicitly their $ K $-theory and deduce in the unimodular case that the corresponding reduced $ C^* $-algebras do not contain nontrivial idempotents. Our approach is based on the reformulation of the Baum-Connes conjecture by Meyer and Nest using the language of triangulated categories. An important ingredient is the theory of monoidal equivalence of compact quantum groups developed by Bichon, De Rijdt and Vaes. This allows us to study the problem in terms of the quantum group $ SU_q(2) $. The crucial part of the argument is a detailed analysis of the equivariant Kasparov theory of the standard Podle\\'s sphere.
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
A chaos-based quantum group signature scheme in quantum cryptosystem
Institute of Scientific and Technical Information of China (English)
娄小平; 陈志刚; MoonHoLee
2015-01-01
A quantum group signature (QGS) scheme is proposed on the basis of an improved quantum chaotic encryption algorithm using the quantum one-time pad with a chaotic operation string. It involves a small-scale quantum computation network in three phases, i.e. initializing phase, signing phase and verifying phase. In the scheme, a member of the group signs the message on behalf of the group while the receiver verifies the signature’s validity with the aid of the trusty group manager who plays a crucial role when a possible dispute arises. Analysis result shows that the signature can neither be forged nor disavowed by any malicious attackers.
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 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
Group cohomology of the Poincare group and invariant quantum states
Moffat, James; Wang, Charles H -T
2016-01-01
Recently there has been an increasing emphasis on completing Dirac's agenda for Quantum Field Theory through the development of completely finite theories, removing the need for renormalisation processes. A key reason for this is the difficulty of applying such processes to gravity which is inherently self -interacting and non-renormalisable. Additional problems include the current need for high-levels of fine tuning to avoid quadratic divergences in Higgs mass corrections. If Supersymmetry applies, the mass-energies of the superpartners (if they exist) are possibly much larger than initially thought and limit their ability to control loop divergence. This leaves open the possibility of other approaches such as Noncommutative Geometry, incorporating fibre bundle theory. The aim of this paper is to consider these existing `low energy' theories incorporating gravity beyond the Standard Model and to develop a coherent mathematical framework based on modern quantum field theory. A number of new ideas have emerged...
Geometry of quantum group twists, multidimensional Jackson calculus and regularization
Demichev, A P
1995-01-01
We show that R-matricies of all simple quantum groups have the properties which permit to present quantum group twists as transitions to other coordinate frames on quantum spaces. This implies physical equivalence of field theories invariant with respect to q-groups (considered as q-deformed space-time groups of transformations) connected with each other by the twists. Taking into account this freedom we study quantum spaces of the special type: with commuting coordinates but with q-deformed differential calculus and construct GL_r(N) invariant multidimensional Jackson derivatives. We consider a particle and field theory on a two-dimensional q-space of this kind and come to the conclusion that only one (time-like) coordinate proved to be discretized.
Center for Elliptic Quantum Group Eτ,η(sln)
Institute of Scientific and Technical Information of China (English)
ZHAO Shao-You; SHI Kang-Jie; YUE Rui-Hong
2003-01-01
We give the center of the elliptic quantum group in general cases. Based on the dynamical Yang-Baxter relation and the fusion method, we prove that the center commutes with all generators of the elliptic quantum group. Then for a kind of assumed form of these generators, we find that the coefficients of these generators form a new type of closed algebra. We also give the center for the algebra.
Junctions of surface operators and categorification of quantum groups
Chun, Sungbong; Roggenkamp, Daniel
2015-01-01
We show how networks of Wilson lines realize quantum groups U_q(sl(m)), for arbitrary m, in 3d SU(N) Chern-Simons theory. Lifting this construction to foams of surface operators in 4d theory we find that rich structure of junctions is encoded in combinatorics of planar diagrams. For a particular choice of surface operators we reproduce known mathematical constructions of categorical representations and categorified quantum groups.
Knot polynomial identities and quantum group coincidences
Morrison, Scott; Snyder, Noah
2010-01-01
We construct link invariants using the D_2n subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories involving the even parts of the D_2n planar algebras. We discuss the origins of these coincidences, explaining the role of SO level-rank duality, Kirby-Melvin symmetry, and properties of small Dynkin diagrams. One of these coincidences involves G_2 and does not appear to be related to level-rank duality.
Doubles of Quasi-Quantum Groups
Hausser, F; Hausser, Frank; Nill, Florian
1999-01-01
Drinfeld showed that any finite dimensional Hopf algebra \\G extends to a quasitriangular Hopf algebra \\D(\\G), the quantum double of \\G. Based on the construction of a so--called diagonal crossed product developed by the authors, we generalize this result to the case of quasi--Hopf algebras \\G. As for ordinary Hopf algebras, as a vector space the ``quasi--quantum double'' \\D(\\G) is isomorphic to the tensor product of \\G and its dual \\dG. We give explicit formulas for the product, the coproduct, the R--matrix and the antipode on quasi--Hopf algebra. In particular \\D(\\G) becomes an associative algebra containing \\G as a quasi--Hopf subalgebra. On the other hand, \\dG øtimes 1 is not a subalgebra of \\D(\\G) unless the coproduct on \\G is strictly coassociative. It is shown that the category of finite dimensional representations of \\D(\\G) coincides with what has been called the double category of \\G--modules by S. Majid [M2]. Thus our construction gives a concrete realization of Majid's abstract definition of quasi-...
Reducibility of quantum representations of mapping class groups
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Fjelstad, Jens
2010-01-01
In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove that the qu......In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove...... 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...
Generalized virtual braid groups, quasi-shuffle product and quantum groups
Fang, Xin
2013-01-01
We introduce in this paper the generalized virtual braid group on n strands GVB_n, generalizing simultaneously the braid groups and their virtual versions. A Mastumoto-Tits type section lifting shuffles in a symmetric group S_n to the monoid associated to GVB_n is constructed, which is then applied to characterize the quantum quasi-shuffle product. A family of representations of GVB_n is constructed using quantum groups.
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.
Quantum cosmology from group field theory condensates: a review
Gielen, Steffen
2016-01-01
We give, in some detail, a critical overview over recent work towards deriving a cosmological phenomenology from the fundamental quantum dynamics of group field theory (GFT), based on the picture of a macroscopic universe as a "condensate" of a large number of quanta of geometry which are given by excitations of the GFT field over a "no-space" vacuum. We emphasise conceptual foundations, relations to other research programmes in GFT and the wider context of loop quantum gravity (LQG), and connections to the quantum physics of real Bose-Einstein condensates. We show how to extract an effective dynamics for GFT condensates from the microscopic GFT physics, and how to compare it with predictions of more conventional quantum cosmology models, in particular loop quantum cosmology (LQC). No detailed familiarity with the GFT formalism is assumed.
Quantum traces for representations of surface groups in SL_2
Bonahon, Francis
2010-01-01
We consider two different quantizations of the character variety consisting of all representations of surface groups in SL_2. One is the skein algebra considered by Przytycki-Sikora and Turaev. The other is the quantum Teichmuller space introduced by Chekhov-Fock and Kashaev. We construct a homomorphism from the skein algebra to the quantum Teichmuller space which, when restricted the classical case, corresponds to the equivalence between these two algebras through trace functions.
Quantum Measurements and the kappa--Poincare Group
Camacho, A; Camacho, Abel
2005-01-01
The possible description of the vacuum of quantum gravity through the so called kappa--Poincare group is analyzed considering some of the consequences of this symmetry in the path integral formulation of nonrelativistic quantum theory. This study is carried out with two cases, firstly, a free particle, and finally, the situation of a particle immersed in a homogeneous gravitational field. It will be shown that the kappa--Poincare group implies the loss of some of the basic properties associated to Feynman's path integral. For instance, loss of the group characteristic related to the time dependence of the evolution operator, or the breakdown of the composition law for amplitudes of events occurring successively in time. Additionally some similarities between the present idea and the so called restricted path integral formalism will be underlined. These analogies advocate the claim that if the kappa--Poincare group contains some of the physical information of the quantum gravity vacuum, then this vacuum could ...
Quantum mechanical behaviour of deuterated methyl groups
Heuer, A.
1992-01-01
We discuss the temperature dependence of deuterium NMR spectra and spin-lattice relaxation rates 1/T 1 of deuterated methyl groups. We restrict ourselves to the temperature range where it is sufficient to consider only the two lowest librational levels of the CD3 group. Specifically we derive explicit expressions for 1/T 1 and the widthГ NMR of the so-called tunneling resonances in the high-field NMR spectrum in the limit where the tunneling frequencyΔ 0 is large compared to the quadrupole co...
Basis Optimization Renormalization Group for Quantum Hamiltonian
Sugihara, Takanori
2001-01-01
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective Hamiltonian. We define two types of rotations and combine them to create appropriate orthogonal transformation.
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
The Problem of Differential Calculus on Quantum Groups
Delius, G W
1996-01-01
The bicovariant differential calculi on quantum groups of Woronowicz have the drawback that their dimensions do not agree with that of the corresponding classical calculus. In this paper we discuss the first-order differential calculus which arises from a simple quantum Lie algebra. This calculus has the correct dimension and is shown to be bicovariant and complete. But it does not satisfy the Leibniz rule. For sl_n this approach leads to a differential calculus which satisfies a simple generalization of the Leibniz rule.
Digital calculus and finite groups in quantum mechanics
Garcia-Morales, Vladimir
2015-01-01
By means of a digit function that has been introduced in a recent formulation of classical and quantum mechanics, we provide a new construction of some infinite families of finite groups, both abelian and nonabelian, of importance for theoretical, atomic and molecular physics. Our construction is not based on algebraic relationships satisfied by generators, but in establishing the appropriate law of composition that induces the group structure on a finite set of nonnegative integers (the cardinal of the set being equal to the order of the group) thus making computations with finite groups quite straightforward. We establish the abstract laws of composition for infinite families of finite groups including all cyclic groups (and any direct sums of them), dihedral, dicyclic and other metacyclic groups, the symmetric groups of permutations of $p$ symbols and the alternating groups of even permutations. Specific examples are given to illustrate the expressions for the law of composition obtained in each case.
Nanomembrane-based materials for Group IV semiconductor quantum electronics.
Paskiewicz, D M; Savage, D E; Holt, M V; Evans, P G; Lagally, M G
2014-02-27
Strained-silicon/relaxed-silicon-germanium alloy (strained-Si/SiGe) heterostructures are the foundation of Group IV-element quantum electronics and quantum computation, but current materials quality limits the reliability and thus the achievable performance of devices. In comparison to conventional approaches, single-crystal SiGe nanomembranes are a promising alternative as substrates for the epitaxial growth of these heterostructures. Because the nanomembrane is truly a single crystal, in contrast to the conventional SiGe substrate made by compositionally grading SiGe grown on bulk Si, significant improvements in quantum electronic-device reliability may be expected with nanomembrane substrates. We compare lateral strain inhomogeneities and the local mosaic structure (crystalline tilt) in strained-Si/SiGe heterostructures that we grow on SiGe nanomembranes and on compositionally graded SiGe substrates, with micro-Raman mapping and nanodiffraction, respectively. Significant structural improvements are found using SiGe nanomembranes.
Group field cosmology: a cosmological field theory of quantum geometry
Calcagni, Gianluca; Oriti, Daniele
2012-01-01
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted to a field, the coordinates are minisuperspace variables, the kinetic operator is the Hamiltonian constraint operator, and the action features a nonlinear and possibly nonlocal interaction term. We discuss free-field classical solutions, the quantum propagator, and a mean-field approximation linearizing the equation of motion and augmenting the Hamiltonian constraint by an effective term mixing gravitational and matter variables. Depending on the choice of interaction, this can reproduce, for example, a cosmological constant, a scalar-field potential, or a curvature contribution.
A group of invariance transformations for nonrelativistic quantum mechanics
Galvan, B
2000-01-01
This paper defines, on the Galilean space-time, the group of asymptoticallyEuclidean transformations (AET), which are equivalent to Euclideantransformations at space-time infinity, and proposes a formulation ofnonrelativistic quantum mechanics which is invariant under suchtransformations. This formulation is based on the asymptotic quantum measure,which is shown to be invariant under AET's. This invariance exposes animportant connection between AET's and Feynman path integrals, and reveals thenonmetric character of the asymptotic quantum measure. The latter featurebecomes even clearer when the theory is formulated in terms of thecoordinate-free formalism of asymptotically Euclidean manifold, which do nothave a metric structure. This mathematical formalism suggests the followingphysical interpretation: (i) Particles evolution is represented by trajectorieson an asymptotically Euclidean manifold; (ii) The metric and the law of motionare not defined a priori as fundamental entities, but they are properties of ap...
The density matrix renormalization group for ab initio quantum chemistry
Wouters, Sebastian
2014-01-01
During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. The MPS ansatz naturally captures exponentially decaying correlation functions. Therefore DMRG works extremely well for noncritical one-dimensional systems. The active orbital spaces in quantum chemistry are however often far from one-dimensional, and relatively large virtual dimensions are required to use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its computational cost, and its properties are discussed. Two important aspects to reduce the computational co...
Curved momentum spaces from quantum groups with cosmological constant
Ballesteros, Á.; Gubitosi, G.; Gutiérrez-Sagredo, I.; Herranz, F. J.
2017-10-01
We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant Λ. In particular, the momentum space associated to the κ-deformation of the de Sitter algebra in (1 + 1) and (2 + 1) dimensions is explicitly constructed as a dual Poisson-Lie group manifold parametrized by Λ. Such momentum space includes both the momenta associated to spacetime translations and the 'hyperbolic' momenta associated to boost transformations, and has the geometry of (half of) a de Sitter manifold. Known results for the momentum space of the κ-Poincaré algebra are smoothly recovered in the limit Λ → 0, where hyperbolic momenta decouple from translational momenta. The approach here presented is general and can be applied to other quantum deformations of kinematical symmetries, including (3 + 1)-dimensional ones.
Canonical Group Quantization, Rotation Generators and Quantum Indistinguishability
Benavides, C
2008-01-01
Using the method of canonical group quantization, we construct the angular momentum operators associated to configuration spaces with the topology of (i) a sphere and (ii) a projective plane. In the first case, the obtained angular momentum operators are the quantum version of Poincare's vector, i.e., the physically correct angular momentum operators for an electron coupled to the field of a magnetic monopole. In the second case, the obtained operators represent the angular momentum operators of a system of two indistinguishable spin zero quantum particles in three spatial dimensions. We explicitly show how our formalism relates to the one developed by Berry and Robbins. The relevance of the proposed formalism for an advance in our understanding of the spin-statistics connection in non-relativistic quantum mechanics is discussed.
The real symplectic groups in quantum mechanics and optics
Dutta, B; Simon, R
1995-01-01
We present a utilitarian review of the family of matrix groups Sp(2n,\\Re)\\/, in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of Sp(2n,\\Re)\\/. Global decomposition theorems, interesting subgroups and their generators are described. Turning to n-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and develop a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under Sp(2n,\\Re)\\/ action are delineated.
Bicovariant calculus on twisted ISO(n), quantum Poincaré group and quantum Minkowski space
Aschieri, Paolo; Aschieri, Paolo; Castellani, Leonardo
1996-01-01
A bicovariant calculus on the twisted inhomogeneous multiparametric q-groups of the B_n,C_n,D_n type, and on the corresponding quantum planes, is found by means of a projection from the bicovariant calculus on B_{n+1}, C_{n+1}, D_{n+1}. In particular we obtain the bicovariant calculus on a dilatation-free q-Poincar\\'e group ISO_q (3, 1), and on the corresponding quantum Minkowski space. The classical limit of the B_n,C_n,D_n bicovariant calculus is discussed in detail.
Multi-group dynamic quantum secret sharing with single photons
Liu, Hongwei; Ma, Haiqiang; Wei, Kejin; Yang, Xiuqing; Qu, Wenxiu; Dou, Tianqi; Chen, Yitian; Li, Ruixue; Zhu, Wu
2016-07-01
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.
Numerical renormalization group method for quantum impurity systems
Bulla, Ralf; Costi, Theo A.; Pruschke, Thomas
2008-04-01
In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.
Cohomology for infinitesimal unipotent algebraic and quantum groups
Drupieski, Christopher M; Ngo, Nham V
2010-01-01
In this paper we study the structure of cohomology spaces for the Frobenius kernels of unipotent and parabolic algebraic group schemes and of their quantum analogs. Given a simple algebraic group $G$, a parabolic subgroup $P_J$, and its unipotent radical $U_J$, we determine the ring structure of the cohomology ring $H^\\bullet((U_J)_1,k)$. We also obtain new results on computing $H^\\bullet((P_J)_1,L(\\lambda))$ as an $L_J$-module where $L(\\lambda)$ is a simple $G$-module with high weight $\\lambda$ in the closure of the bottom $p$-alcove. Finally, we provide generalizations of all our results to the quantum situation.
Yang-Baxter algebras, integrable theories and quantum groups
Energy Technology Data Exchange (ETDEWEB)
Vega, H.J. de (Paris-6 Univ., 75 (France). Lab. de Physique Theorique et Hautes Energies)
1990-12-01
The Yang-Baxter algebras (YBA) are introduced in a general framework stressing their power to exactly solve the lattice models associated to them. The algebraic Bethe Ansatz is developed as an eigenvector construction based on the YBA. The six-vertex model solution is given explicitely. It is explained how these lattice models yield both solvable massive QFT and conformal models in appropriated scaling (continuous) limits within the lattice light-cone approach. This approach permit to define and solve rigorously massive QFT as an appropriate continuum limit of gapless vertex models. The deep links between the YBA and Lie algebras are analyzed including the quantum groups that underly the trigonometric/hyperbolic YBA. Braid and quantum groups are derived from trigonometric/hyperbolic YBA in the limit of infinite spectral parameter. To conclude, some recent developments in the domain of integrable theories are summarized. (orig.).
On kappa-deformed D=4 quantum conformal group
Kosi'nski, P; Maslanka, P
2003-01-01
This paper is presented on the occasion of 60-th birthday of Jose Adolfo de Azcarraga who in his very rich scientific curriculum vitae has also a chapter devoted to studies of quantum-deformed symmetries, in particular deformations of relativistic and Galilean space-time symmetries [1-4]. In this paper we provide new steps toward describing the $\\kappa$-deformed D=4 conformal group transformations. We consider the quantization of D=4 conformal group with dimensionful deformation parameter $\\kappa$. Firstly we discuss the noncommutativity following from the Lie-Poisson structure described by the light-cone $\\kappa$-Poincar\\'{e} $r$-matrix. We present complete set of D=4 conformal Lie-Poisson brackets and discuss their quantization. Further we define the light-cone $\\kappa$-Poincar\\'{e} quantum $R$-matrix in O(4,2) vector representation and discuss the inclusion of noncommutative conformal translations into the framework of $\\kappa$-deformed conformal quantum group. The problem with real structure of $\\kappa$-d...
The Representations of Quantum Double of Dihedral Groups
Dong, Jingcheng
2011-01-01
Let $k$ be an algebraically closed field of odd characteristic $p$, and let $D_n$ be the dihedral group of order $2n$ such that $p\\mid 2n$. Let $D(kD_n)$ denote the quantum double of the group algebra $kD_n$. In this paper, we describe the structures of all finite dimensional indecomposable left $D(kD_n)$-modules, equivalently, of all finite dimensional indecomposable Yetter-Drinfeld $kD_n$-modules, and classify them.
Geometry of q-Hypergeometric Functions, Quantum Affine Algebras and Elliptic Quantum Groups
Tarasov, V; Tarasov, Vitaly; Varchenko, Alexander
1997-01-01
The trigonometric quantized Knizhnik-Zamolodchikov equation (qKZ equation) associated with the quantum group $U_q(sl_2)$ is a system of linear difference equations with values in a tensor product of $U_q(sl_2)$ Verma modules. We solve the equation in terms of multidimensional $q$-hypergeometric functions and define a natural isomorphism between the space of solutions and the tensor product of the corresponding evaluation Verma modules over the elliptic quantum group $E_{\\rho,\\gamma}(sl_2)$, where parameters $\\rho$ and $\\gamma$ are related to the parameter $q$ of the quantum group $U_q(sl_2)$ and the step $p$ of the qKZ equation via $p=e^{2\\pii\\rho}$ and $q=e^{-2\\pii\\gamma}$. We construct asymptotic solutions associated with suitable asymptotic zones and compute the transition functions between the asymptotic solutions in terms of the dynamical elliptic $R$-matrices. This description of the transition functions gives a connection between representation theories of the quantum loop algebra $U_q(\\widetilde{gl}_2...
Quasi-Hopf twistors for elliptic quantum groups
Jimbo, M; Odake, S; Shiraishi, J
1997-01-01
The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al., Felder). Fronsdal made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum affine algebra U_q(g). In this paper we present an explicit formula for the twistors in the form of an infinite product of the universal R matrix of U_q(g). We also prove the shifted cocycle condition for the twistors, thereby completing Fronsdal's findings. This construction entails that, for generic values of the deformation parameters, representation theory for U_q(g) carries over to the elliptic algebras, including such objects as evaluation modules, highest weight modules and vertex operators. In particular, we confirm the conjectures of Foda et al. concerning the elliptic algebra A_{q,p}(^sl_2).
Q-bosonization of the quantum group GL$_{q}$(2) based on the Gauss decomposition
Damaskinsky, E V; Damaskinsky, E V; Sokolov, M A
1995-01-01
The new method of q-bosonization for quantum groups based on the Gauss decomposition of a transfer matrix of generators is suggested. The simplest example of the quantum group GL_q(2) is considered in some details.
Twisting 2-cocycles for the construction of new non-standard quantum groups
Jacobs, A D; Jacobs, Andrew D.
1997-01-01
We introduce a new class of 2-cocycles defined explicitly on the generators of certain multiparameter standard quantum groups. These allow us, through the process of twisting the familiar standard quantum groups, to generate new as well as previously known examples of non-standard quantum groups. In particular we are able to construct generalizations of both the Cremmer-Gervais deformation of SL(3), and the so called esoteric quantum groups of Fronsdal and Galindo, in an explicit and straightforward manner.
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.
Positive Casimir and Central Characters of Split Real Quantum Groups
Ip, Ivan C. H.
2016-06-01
We describe the generalized Casimir operators and their actions on the positive representations {mathcal{P}_λ} of the modular double of split real quantum groups {mathcal{U}_{qtilde{q}}(mathfrak{g}_mathbb{R})}. We introduce the notion of virtual highest and lowest weights, and show that the central characters admit positive values for all parameters {λ}. We show that their image defines a semi-algebraic region bounded by real points of the discriminant variety independent of q, and we discuss explicit examples in the lower rank cases.
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.
Construct irreducible representations of quantum groups Uq(fm(K))
Institute of Scientific and Technical Information of China (English)
Xin TANG
2008-01-01
In this paper,we construct families of irreducible representations for a class of quantum groups Uq(fm(K)).First,we give a natural construction of irreducible weight representations for Uq(fm(K)) using methods in spectral theory developed by Rosenberg.Second,we study the Whittaker model for the center of Uq(fm(K)).As a result,the structure of Whittaker representations is determined,and all irreducible Whittaker representations are explicitly constructed.Finally,we prove that the annihilator of a Whittaker representation is centrally generated.
Controlling group velocity in a superconductive quantum circuit
Institute of Scientific and Technical Information of China (English)
Qiu Tian-Hui; Yang Guo-Jian
2012-01-01
We investigate the controllable group velocity of a microwave probe field in a superconductive quantum circuit (SQC) pumped by microwave fields,and the use of such a SQC function as an artificial A-type three-level atom.The exchange between the subluminal and the superluminal states of the probe field can be realized simply by sweeping the pumping intensity,and the superluminal state is usually realized with a lower absorption.This work is one of the efforts to extend the study of electromagnetically induced transparency and its related properties from the lightwave band to the microwave band.
Brownian motion on Lie groups and open quantum systems
Energy Technology Data Exchange (ETDEWEB)
Aniello, P; Marmo, G; Ventriglia, F [Dipartimento di Scienze Fisiche dell' Universita di Napoli ' Federico II' and Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, I-80126 Napoli (Italy); Kossakowski, A, E-mail: paolo.aniello@na.infn.i, E-mail: kossak@fyzika.umk.p, E-mail: marmo@na.infn.i, E-mail: ventriglia@na.infn.i [MECENAS, Universita di Napoli ' Federico II' , via Mezzocannone 8, I-80134 Napoli (Italy)
2010-07-02
We study the twirling semigroups of (super) operators, namely certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution semigroup of probability measures on this group. The link connecting this class of semigroups of operators with (classical) Brownian motion is clarified. It turns out that every twirling semigroup associated with a finite-dimensional representation is a random unitary semigroup, and, conversely, every random unitary semigroup arises as a twirling semigroup. Using standard tools of the theory of convolution semigroups of measures and of convex analysis, we provide a complete characterization of the infinitesimal generator of a twirling semigroup associated with a finite-dimensional unitary representation of a Lie group.
Brownian motion on Lie groups and open quantum systems
Aniello, P.; Kossakowski, A.; Marmo, G.; Ventriglia, F.
2010-07-01
We study the twirling semigroups of (super) operators, namely certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution semigroup of probability measures on this group. The link connecting this class of semigroups of operators with (classical) Brownian motion is clarified. It turns out that every twirling semigroup associated with a finite-dimensional representation is a random unitary semigroup, and, conversely, every random unitary semigroup arises as a twirling semigroup. Using standard tools of the theory of convolution semigroups of measures and of convex analysis, we provide a complete characterization of the infinitesimal generator of a twirling semigroup associated with a finite-dimensional unitary representation of a Lie group.
Brownian motion on Lie groups and open quantum systems
Aniello, P; Marmo, G; Ventriglia, F
2010-01-01
We study the twirling semigroups of (super)operators, namely, certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution semigroup of probability measures on this group. The link connecting this class of semigroups of operators with (classical) Brownian motion is clarified. It turns out that every twirling semigroup associated with a finite-dimensional representation is a random unitary semigroup, and, conversely, every random unitary semigroup arises as a twirling semigroup. Using standard tools of the theory of convolution semigroups of measures and of convex analysis, we provide a complete characterization of the infinitesimal generator of a twirling semigroup associated with a finite-dimensional unitary representation of a Lie group.
Encoding simplicial quantum geometry in group field theories
Energy Technology Data Exchange (ETDEWEB)
Oriti, D [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany); Tlas, T, E-mail: daniele.oriti@aei.mpg.d, E-mail: tamer.tlas@aub.edu.l [Department of Mathematics, American Univeristy of Beirut, Bliss Street, Beirut, PO Box 11-0236 (Lebanon)
2010-07-07
An extended group field theory formalism for quantum gravity, based on a field that is a function of both group variables, interpreted as discretized connection, and Lie algebra variables, interpreted as discretized triads, has been proposed recently as an attempt to define models with a clearer link with simplicial geometry. In the context of such a formalism, we introduce a new symmetry requirement on the field. This leads, in 3D, to Feynman amplitudes interpreted as simplicial path integrals based on the Regge action, to a proper relation between the discrete connection and the triad vectors appearing in the Regge action, and to a much more satisfactory and transparent encoding of simplicial geometry already at the level of the group field theory action.
Renormalization group approach to scalar quantum electrodynamics on de Sitter
González, Francisco Fabián
2016-01-01
We consider the quantum loop effects in scalar electrodynamics on de Sitter space by making use of the functional renormalization group approach. We first integrate out the photon field, which can be done exactly to leading (zeroth) order in the gradients of the scalar field, thereby making this method suitable for investigating the dynamics of the infrared sector of the theory. Assuming that the scalar remains light we then apply the functional renormalization group methods to the resulting effective scalar theory and focus on investigating the effective potential, which is the leading order contribution in the gradient expansion of the effective action. We find symmetry restoration at a critical renormalization scale $\\kappa=\\kappa_{\\rm cr}$ much below the Hubble scale $H$. When compared with the results of Serreau and Guilleux [arXiv:1306.3846 [hep-th], arXiv:1506.06183 [hep-th
Module homomorphisms and multipliers on locally compact quantum groups
Ramezanpour, M
2009-01-01
For a Banach algebra $A$ with a bounded approximate identity, we investigate the $A$-module homomorphisms of certain introverted subspaces of $A^*$, and show that all $A$-module homomorphisms of $A^*$ are normal if and only if $A$ is an ideal of $A^{**}$. We obtain some characterizations of compactness and discreteness for a locally compact quantum group $\\G$. Furthermore, in the co-amenable case we prove that the multiplier algebra of $\\LL$ can be identified with $\\MG.$ As a consequence, we prove that $\\G$ is compact if and only if $\\LUC={\\rm WAP}(\\G)$ and $\\MG\\cong\\mathcal{Z}({\\rm LUC}(\\G)^*)$; which partially answer a problem raised by Volker Runde.
Numerical renormalization group for quantum impurities in a bosonic bath
Bulla, Ralf; Lee, Hyun-Jung; Tong, Ning-Hua; Vojta, Matthias
2005-01-01
We present a detailed description of the recently proposed numerical renormalization group method for models of quantum impurities coupled to a bosonic bath. Specifically, the method is applied to the spin-boson model, both in the Ohmic and sub-Ohmic cases. We present various results for static as well as dynamic quantities and discuss details of the numerical implementation, e.g., the discretization of a bosonic bath with arbitrary continuous spectral density, the suitable choice of a finite basis in the bosonic Hilbert space, and questions of convergence with respect to truncation parameters. The method is shown to provide high-accuracy data over the whole range of model parameters and temperatures, which are in agreement with exact results and other numerical data from the literature.
Aperiodic quantum XXZ chains: Renormalization-group results
Vieira, André P.
2005-04-01
We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations of chains with couplings following several two-letter aperiodic sequences, including the quasiperiodic Fibonacci and other precious-mean sequences, as well as sequences inducing strong geometrical fluctuations. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. We also discuss the nature of the ground-state structures and their comparison with the random-singlet phase characteristic of random-bond chains.
Locally Compact Quantum Groups. A von Neumann Algebra Approach
Van Daele, Alfons
2014-08-01
In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We start with a von Neumann algebra and a comultiplication on this von Neumann algebra. We assume that there exist faithful left and right Haar weights. Then we develop the theory within this von Neumann algebra setting. In [Math. Scand. 92 (2003), 68-92] locally compact quantum groups are also studied in the von Neumann algebraic context. This approach is independent of the original C^*-algebraic approach in the sense that the earlier results are not used. However, this paper is not really independent because for many proofs, the reader is referred to the original paper where the C^*-version is developed. In this paper, we give a completely self-contained approach. Moreover, at various points, we do things differently. We have a different treatment of the antipode. It is similar to the original treatment in [Ann. Sci. & #201;cole Norm. Sup. (4) 33 (2000), 837-934]. But together with the fact that we work in the von Neumann algebra framework, it allows us to use an idea from [Rev. Roumaine Math. Pures Appl. 21 (1976), 1411-1449] to obtain the uniqueness of the Haar weights in an early stage. We take advantage of this fact when deriving the other main results in the theory. We also give a slightly different approach to duality. Finally, we collect, in a systematic way, several important formulas. In an appendix, we indicate very briefly how the C^*-approach and the von Neumann algebra approach eventually yield the same objects. The passage from the von Neumann algebra setting to the C^*-algebra setting is more or less standard. For the other direction, we use a new method. It is based on the observation that the Haar weights on the C^*-algebra extend to weights on the double dual with central support and that all these supports are the same. Of course, we get the von Neumann algebra by cutting down the double dual with this unique
Minimum uncertainty states for the quantum group SU{sub q}(2) and quantum Wigner d-functions
Energy Technology Data Exchange (ETDEWEB)
Mann, A.; Parthasarathy, R. [Institute of Mathematical Sciences, Madras (India)
1996-01-21
Minimum uncertainty angular momentum states for the quantum group SU{sub q}(2) are constructed. They involve the eigenvalues of J{sub 1} which are q-numbers and the quantum group analogue of the Wigner d-functions for {theta}={pi}/2. The result is generalized for all values of {theta} and a formula for the quantum Wigner d-function is derived. The case of q=1 is discussed and compared with the well known results for the Wigner d-functions. (author)
Quantum groups and functional relations for lower rank
Nirov, Kh. S.; Razumov, A. V.
2017-02-01
A detailed construction of the universal integrability objects related to the integrable systems associated with the quantum loop algebra Uq(L(sl2)) is given. The full proof of the functional relations in the form independent of the representation of the quantum loop algebra on the quantum space is presented. The case of the general gradation and general twisting is treated. The specialization of the universal functional relations to the case when the quantum space is the state space of a discrete spin chain is described. This is a digression of the corresponding consideration for the case of the quantum loop algebra Uq(L(sl3)) with an extension to the higher spin case.
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.
From exponential coordinates to bicovariant differential calculi on matrix quantum groups
Hijligenberg, N.W. van den; Martini, R.
1995-01-01
A procedure to obtain bicovariant differential calculi on matrix quantum groups is presented. The construction is based on the description of the matrix quantum group as a quantized universal enveloping algebra by the use of exponential coordinates. The procedure is illustrated by applying it to the
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
L^2-Betti numbers of rigid C*-tensor categories and discrete quantum groups (preprint)
DEFF Research Database (Denmark)
Kyed, David; Raum, Sven; Vaes, Stefaan;
2017-01-01
We compute the $L^2$-Betti numbers of the free $C^*$-tensor categories, which are the representation categories of the universal unitary quantum groups $A_u(F)$. We show that the $L^2$-Betti numbers of the dual of a compact quantum group $G$ are equal to the $L^2$-Betti numbers of the representat...
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 a
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 a
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...
The genus one Complex Quantum Chern-Simons representation of the Mapping Class Group
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Marzioni, Simone
In this paper we compute explicitly, following Witten’s prescription, the quantum representation of the mapping class group in genus one for complex quantum Chern-Simons theory associated to the complex gauge group SL(2, C). We use the k’th order Weil-Gel’fand-Zak transform to exhibit an explicit...
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.
The symmetry groups of noncommutative quantum mechanics and coherent state quantization
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, S. Hasibul Hassan; Ali, S. Twareque [Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8 (Canada)
2013-03-15
We explore the group theoretical underpinning of noncommutative quantum mechanics for a system moving on the two-dimensional plane. We show that the pertinent groups for the system are the two-fold central extension of the Galilei group in (2+1)-space-time dimensions and the two-fold extension of the group of translations of R{sup 4}. This latter group is just the standard Weyl-Heisenberg group of standard quantum mechanics with an additional central extension. We also look at a further extension of this group and discuss its significance to noncommutative quantum mechanics. We build unitary irreducible representations of these various groups and construct the associated families of coherent states. A coherent state quantization of the underlying phase space is then carried out, which is shown to lead to exactly the same commutation relations as usually postulated for this model of noncommutative quantum mechanics.
Pendás, A Martín; Francisco, E; Blanco, M A
2007-01-01
We analyze the response of a quantum group within a molecule to charge transfer by using the interacting quantum atoms approach (IQA), an energy partitioning scheme within the quantum theory of atoms in molecules (QTAM). It is shown that this response lies at the core of the concept of the functional group. The manipulation of fractional electron populations is carried out by using distribution functions for the electron number within the quantum basins. Several test systems are studied to show that similar chemical potential groups are characterized by similar energetic behavior upon interaction with other groups. The origin of the empirical additivity rules for group energies in simple hydrocarbons is also investigated. It turns out to rest on the independent saturation of both the self-energies and the interaction energies of the groups as the size of the chain increases. We also show that our results are compatible with the standard group energies of the QTAM.
Yang-Baxter Maps, Discrete Integrable Equations and Quantum Groups
Bazhanov, Vladimir V
2015-01-01
For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang-Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper...
Quantum spins and quasiperiodicity: a real space renormalization group approach.
Jagannathan, A
2004-01-30
We study the antiferromagnetic spin-1/2 Heisenberg model on a two-dimensional bipartite quasiperiodic structure, the octagonal tiling, the aperiodic equivalent of the square lattice for periodic systems. An approximate block spin renormalization scheme is described for this problem. The ground state energy and local staggered magnetizations for this system are calculated and compared with the results of a recent quantum Monte Carlo calculation for the tiling. It is conjectured that the ground state energy is exactly equal to that of the quantum antiferromagnet on the square lattice.
Free Fermionic Elliptic Reflection Matrices and Quantum Group Invariance
Cuerno, R
1993-01-01
Elliptic diagonal solutions for the reflection matrices associated to the elliptic $R$ matrix of the eight vertex free fermion model are presented. They lead through the second derivative of the open chain transfer matrix to an XY hamiltonian in a magnetic field which is invariant under a quantum deformed Clifford--Hopf algebra.
Global dimensions for Lie groups at level k and their conformally exceptional quantum subgroups
Coquereaux, Robert
2010-01-01
We obtain formulae giving global dimensions for fusion categories defined by Lie groups G at level k and for the associated module-categories obtained via conformal embeddings. The results can be expressed in terms of Lie quantum superfactorials of type G. The later are related, for the type Ar, to the quantum Barnes function.
An introduction to non-commutative differential geometry on quantum groups
Aschieri, Paolo
1993-01-01
We give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case ($q \\rightarrow 1$ limit). The Lie derivative and the contraction operator on forms and tensor fields are found. A new, explicit form of the Cartan--Maurer equations is presented. The example of a bicovariant differential calculus on the quantum group $GL_q(2)$ is given in detail. The softening of a quantum group is considered, and we introduce $q$-curvatures satisfying q-Bianchi identities, a basic ingredient for the construction of $q$-gravity and $q$-gauge theories.
Group Theoretical Approach for Controlled Quantum Mechanical Systems
2007-11-06
evolution equation with Hamiltonians which may possess discrete , continuous, and mixed spectrum. For such a quantum system, the Hamiltonian operator...study of classical linear and nonlinear systems, which proves to be very useful in understanding the design problems such as disturbance decoupling...developed by Kunita can then be implemented to establish controllability conditions for the original time-dependent Schrodinger control problem. The end
Azam, Saeid; Yousofzadeh, Malihe
2011-01-01
We classify finite-dimensional irreducible highest weight modules of generalized quantum groups whose positive part is infinite dimensional and has a Kharchenko's PBW basis with an irreducible finite positive root system.
A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
Oriti, D; Tlas, T.
2007-01-01
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 amplitudes are given by path integrals for clearly identified discrete gravity actions, in 1st order variables. In the 3-dimensional case, the corresponding discrete action is that of 1st order Regg...
Group III-nitride based hetero and quantum structures
Monemar, B.; Pozina, G.
2000-11-01
The present paper attempts an overview of a presently very active research field: the III-nitrides and their interesting possibilities for a range of device applications employing heterostructures and low-dimensional quantum structures. The family of materials containing AlN, GaN, InN and the alloys between them span a range of direct bandgaps between 6.2 and 1.9 eV, with very large band offsets in type I heterojunctions, which is very favourable for a number of interesting device concepts. A very important feature of these materials is the dominant influence of strong polarisation fields (spontaneous as well as piezo-electric) on the physical properties of multilayer structures, as well as on devices. Exciton binding energies are large, and excitonic effects are therefore important at room temperature. Many alloy systems, in particular InGaN, have a high miscibility gap, leading to a strong tendency for phase separation and consequently to many novel physical properties which yet have to be explored in detail. Localization effects for carriers and excitons are very important in quantum structures based on these alloys. Devices based on III-N heterostructures cover a wide range, from optical devices (violet lasers, LEDs covering a range from UV to red, white LEDs, photodetectors, UV cameras) to high-frequency power devices, both unipolar transistors (AlGaN/GaN HEMTs) and bipolar HBTs.
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.
A new class of group field theories for first order discrete quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Oriti, D [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, Utrecht 3584 TD (Netherlands); Tlas, T [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)], E-mail: d.oriti@phys.uu.nl, E-mail: t.tlas@damtp.cam.ac.uk
2008-04-21
Group field theories, a generalization of matrix models for 2D gravity, represent a second 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 amplitudes are given by path integrals for clearly identified discrete gravity actions, in first order variables. In the three-dimensional case, the corresponding discrete action is that of first order Regge calculus for gravity (generalized to include higher order corrections), while in higher dimensions, they correspond to a discrete BF theory (again, generalized to higher order) with an imposed orientation restriction on hinge volumes, similar to that characterizing discrete gravity. This new class of group field theories may represent a concrete unifying framework for loop quantum gravity and simplicial quantum gravity approaches.
A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
Oriti, Daniele
2007-01-01
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 amplitudes are given by path integrals for clearly identified discrete gravity actions, in 1st order variables. In the 3-dimensional case, the corresponding discrete action is that of 1st order Regge calculus for gravity (generalized to include higher order corrections), while in higher dimensions, they correspond to a discrete BF-theory (again, generalized to higher order) with an imposed orientation restriction on hinge volumes, similar to that characterizing discrete gravity. The new models shed also light on the large distance or semi-classical approximation of spin foam models. This new class of group field theories may represent a concrete unifying framework for loop quantum gravity and simplicial quantum grav...
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.
Quantum Master Equation for QED in Exact Renormalization Group
Igarashi, Yuji; Sonoda, Hidenori
2007-01-01
Recently, one of us (H.S.) gave an explicit form of the Ward-Takahashi identity for the Wilson action of QED. We first rederive the identity using a functional method. The identity makes it possible to realize the gauge symmetry even in the presence of a momentum cutoff. In the cutoff dependent realization, the abelian nature of the gauge symmetry is lost, breaking the nilpotency of the BRS transformation. Using the Batalin-Vilkovisky formalism, we extend the Wilson action by including the antifield contributions. Then, the Ward-Takahashi identity for the Wilson action is lifted to a quantum master equation, and the modified BRS transformation regains nilpotency. We also obtain a flow equation for the extended Wilson action.
Nonstabilizer Quantum Codes from Abelian Subgroups of the Error Group
Arvind, V; Parthasarathy, K R; Kurur, Piyush P
2002-01-01
This paper is motivated by the computer-generated nonadditive ((5,6,2)) code described in an article by Rains, Hardin, Shor and Sloane. We describe a theory of non-stabilizer codes of which the nonadditive code of Rains et al is an example. Furthermore, we give a general strategy of constructing good nonstabilizer codes from good stabilizer codes and give some explicit constructions and asymptotically good nonstabilizer codes. In fact, we explicitly construct a family of distance 2 non-stabilizer codes over all finite fields of which the ((5,6,2)) is an special example. More interestingly, using our theory, we are also able to explicitly construct examples of non-stablizer quantum codes of distance 3. Like in the case of stabilizer codes, we can design fairly efficient encoding and decoding procedures.
Wess, J; Physics Enrico Fermi : Quantum Groups and their Applications in Physics
1996-01-01
This book focuses on quantum groups, i.e., continuous deformations of Lie groups, and their applications in physics. These algebraic structures have been studied in the last decade by a growing number of mathematicians and physicists, and are found to underlie many physical systems of interest. They do provide, in fact, a sort of common algebraic ground for seemingly very different physical problems. As it has happened for supersymmetry, the q-group symmetries are bound to play a vital role in physics, even in fundamental theories like gauge theory or gravity. In fact q-symmetry can be considered itself as a generalization of supersymmetry, evident in the q-commutator formulation. The hope that field theories on q-groups are naturally reguralized begins to appear founded, and opens new perspectives for quantum gravity. The topics covered in this book include: conformal field theories and quantum groups, gauge theories of quantum groups, anyons, differential calculus on quantum groups and non-commutative geome...
Group field theory as the second quantization of loop quantum gravity
Oriti, Daniele
2016-04-01
We construct a second quantized reformulation of canonical loop quantum gravity (LQG) at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the group field theory (GFT) formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.
Elliptic Quantum Groups U_{q,p}(gl_N) and E_{q,p}(gl_N)
Konno, Hitoshi
2016-01-01
We reformurate a central extension of Felder's elliptic quantum group in the FRST formulation as a topological algebra E_{q,p}(gl_N) over the ring of formal power series in p. We then discuss the isomorphism between E_{q,p}(gl_N) and the elliptic algebra U_{q,p}(gl_N) of the Drinfeld realization. An evaluation H-algebra homomorphism from U_{q,p}(gl_N) to a dynamical extension of the quantum affine algebra U_q(gl_N) resolves the problem into the one discussed by Ding and Frenkel in the trigonometric case. We also provide some useful formulas for the elliptic quantum determinants.
Group field theory as the 2nd quantization of Loop Quantum Gravity
Oriti, Daniele
2013-01-01
We construct a 2nd quantized reformulation of canonical Loop Quantum Gravity at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the Group Field Theory formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.
A remark on the motivic Galois group and the quantum coadjoint action
Grosse, H; Grosse, Harald; Schlesinger, Karl-Georg
2004-01-01
It was suggested by Kontsevich that the Grothendieck-Teichmueller group GT should act on the Duflo isomorphism of su(2) but the corresponding realization of GT turned out to be trivial. We show that a solvable quotient of the motivic Galois group - which is supposed to agree with GT - is closely related to the quantum coadjoint action on U_q(sl_2) for q a root of unity, i.e. in the quantum group case one has a nontrivial realization of a quotient of the motivic Galois group. From a discussion of the algebraic properties of this realization we conclude that in more general cases than U_q(sl_2) it should be related to a quantum version of the motivic Galois group. Finally, we discuss the relation of our construction to quantum field and string theory and explain what we believe to be the "physical reason" behind this relation between the motivic Galois group and the quantum coadjoint action. This might be a starting point for the generalization of our construction to more involved examples.
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...
Group field theory as the 2nd quantization of Loop Quantum Gravity
Oriti, Daniele
2013-01-01
We construct a 2nd quantized reformulation of canonical Loop Quantum Gravity at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the Group Field Theory formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specifi...
Baryons from quantum mechanics on the Lie group u(3)
Trinhammer, Ole L
2011-01-01
We develop a hamiltonian framework on the Lie group u(3), which we call allospace and which is supposed to carry all the colour dynamics needed to describe the baryon spectrum. The energy eigenstates of our particular Schr\\"odinger equation tends to predict realistically all certain baryon resonances in the NDelta sector. The grouping and number of resonances is predicted by the model from a single fitting of the ground state N(939). The Hamiltonian also contains terms from the group space Laplacian to take care of the superimposed hypercharge and isospin flavour structure. Scarce neutral flavour singlet resonances are predicted and may show up around 4500 MeV in neutron diffraction dissociation experiments above the threshold in the free charm system Sigmacplus(2455)Dminus . We give a controversial prediction of the neutron-proton mass difference as originating in a period doubling of certain parametric states. The group space dynamics communicates with real space via the exterior derivative which projects o...
A family of affine quantum group invariant integrable extensions of the Hubbard Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Avakyan, A. [Erevanskij Fizicheskij Inst., Erevan (Armenia); Hakobyan, T. [Erevanskij Fizicheskij Inst., Erevan (Armenia); Sedrakyan, A. [Erevanskij Fizicheskij Inst., Erevan (Armenia)
1997-04-21
We construct a family of spin chain Hamiltonians, which have the affine quantum group symmetry U{sub q}g. Their eigenvalues coincide with the eigenvalues of the usual spin chain Hamiltonians, but have the degeneracy of levels, corresponding to the affine U{sub q}g. The space of states of these spin chains is formed by the tensor product of the fully reducible representations of the quantum group. The fermionic representations of the constructed spin chain Hamiltonians show that we have obtained new extensions of the Hubbard Hamiltonians. All of them are integrable and have the affine quantum group symmetry. The exact ground state of such type of model is presented, exhibiting superconducting behavior via the {eta}-pairing mechanism. (orig.).
Functional renormalization group approach to the singlet-triplet transition in quantum dots.
Magnusson, E B; Hasselmann, N; Shelykh, I A
2012-09-12
We present a functional renormalization group approach to the zero bias transport properties of a quantum dot with two different orbitals and in the presence of Hund's coupling. Tuning the energy separation of the orbital states, the quantum dot can be driven through a singlet-triplet transition. Our approach, based on the approach by Karrasch et al (2006 Phys. Rev. B 73 235337), which we apply to spin-dependent interactions, recovers the key characteristics of the quantum dot transport properties with very little numerical effort. We present results on the conductance in the vicinity of the transition and compare our results both with previous numerical renormalization group results and with predictions of the perturbative renormalization group.
Tian, Si-Cong; Wan, Ren-Gang; Ning, Yong-Qiang; Wang, Li-Jun
2013-01-01
We analyze the interaction of a triple quantum dot molecules controlled by the tunneling coupling instead of coupling laser. A general analytic expression for the steady-state linear susceptibility for a probe-laser field is obtained and we show that the system can exhibit two transparency windows. The group velocity of the probe-laser pulse is also analyzed. By changing the tunneling couplings, two laser pulses with different central frequency can propagate with the same group velocity. And the group velocity can be as low as 300 m/s in our system. We extend our analysis to the case of multiple quantum dot molecules (the number of the quantum dots is N) and show that the system can exhibit at most N-1 transparency windows. And at most N-1 laser pulses with different central frequencies can be slowed down.
Protsenko, V. S.; Katanin, A. A.
2017-06-01
We explore the effects of asymmetry of hopping parameters between double parallel quantum dots and the leads on the conductance and a possibility of local magnetic moment formation in this system using functional renormalization group approach with the counterterm. We demonstrate a possibility of a quantum phase transition to a local moment regime [so-called singular Fermi liquid (SFL) state] for various types of hopping asymmetries and discuss respective gate voltage dependencies of the conductance. We show that, depending on the type of the asymmetry, the system can demonstrate either a first-order quantum phase transition to an SFL state, accompanied by a discontinuous change of the conductance, similarly to the symmetric case, or the second-order quantum phase transition, in which the conductance is continuous and exhibits Fano-type asymmetric resonance near the transition point. A semianalytical explanation of these different types of conductance behavior is presented.
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.
Group theory in quantum mechanics an introduction to its present usage
Heine, Volker
1960-01-01
Group Theory in Quantum Mechanics: An Introduction to its Present Usage introduces the reader to the three main uses of group theory in quantum mechanics: to label energy levels and the corresponding eigenstates; to discuss qualitatively the splitting of energy levels as one starts from an approximate Hamiltonian and adds correction terms; and to aid in the evaluation of matrix elements of all kinds, and in particular to provide general selection rules for the non-zero ones. The theme is to show how all this is achieved by considering the symmetry properties of the Hamiltonian and the way in w
Rings of skew polynomials and Gel'fand-Kirillov conjecture for quantum groups
Iohara, Kenji; Malikov, Feodor
1993-01-01
We introduce and study action of quantum groups on skew polynomial rings and related rings of quotients. This leads to a ``q-deformation'' of the Gel'fand-Kirillov conjecture which we partially prove. We propose a construction of automorphisms of certain non-commutaive rings of quotients coming from complex powers of quantum group generators; this is applied to explicit calculation of singular vectors in Verma modules over $U_{q}(\\gtsl_{n+1})$. We finally give a definition of a $q-$connection...
A quantum analogue of the Grothendieck-Teichmueller group
Schlesinger, K G
2002-01-01
We introduce a self-dual, noncommutative and noncocommutative Hopf algebra H sub G sub T which takes for certain Hopf categories (and therefore braided monoidal bicategories) a similar role to the Grothendieck-Teichmueller group for quasitensor categories. We also give a result which highly restricts the possibility for similar structures for higher weak n-categories (n >= 3) by showing that these structures would not allow for any nontrivial deformations. Finally, we give an explicit description of the elements of H sub G sub T.
Multi-proxy quantum group signature scheme with threshold shared verification
Institute of Scientific and Technical Information of China (English)
Yang Yu-Guang
2008-01-01
A multi-proxy quantum group signature scheme with threshold shared verification is proposed.An original signer may authorize a proxy group as his proxy agent.Then only the cooperation of all the signers in the proxy group can generate the proxy signature on behalf of the original signer.In the scheme,any t or more of n receivers can verify the message and any t-1 or fewer receivers cannot verify the validity of the proxy signature.
Quantum automorphisms of twisted group algebras and free hypergeometric laws
Banica, Teodor; Curran, Stephen
2010-01-01
We prove that we have an isomorphism of type $A_{aut}(\\mathbb C_\\sigma[G])\\simeq A_{aut}(\\mathbb C[G])^\\sigma$, for any finite group $G$, and any 2-cocycle $\\sigma$ on $G$. In the particular case $G=\\mathbb Z_n^2$, this leads to a Haar-measure preserving identification between the subalgebra of $A_o(n)$ generated by the variables $u_{ij}^2$, and the subalgebra of $A_s(n^2)$ generated by the variables $X_{ij}=\\sum_{a,b=1}^np_{ia,jb}$. Since $u_{ij}$ is "free hyperspherical" and $X_{ij}$ is "free hypergeometric", we obtain in this way a new free probability formula, which at $n=\\infty$ corresponds to the well-known relation between the semicircle law, and the free Poisson law.
S-Matrices and Quantum Group Symmetry of q-Deformed Sigma Models
Hollowood, Timothy J; Schmidtt, David M
2015-01-01
Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the q-deformations with q a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.
S-matrices and quantum group symmetry of k-deformed sigma models
Hollowood, Timothy J.; Miramontes, J. Luis; Schmidtt, David M.
2016-11-01
Recently, two kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed (Delduc et al 2014 Phys. Rev. Lett. 112 051601; Hollowood et al 2014 J. Phys. A: Math. Theor. 47 495402). One class of these, the k deformations associated to the more general q deformations but with q={{{e}}}{{i}π /k} a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.
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.
Gr(o)bner-Shirshov Basis of Quantum Group of Type D4
Institute of Scientific and Technical Information of China (English)
Gulshadam YUNUS; Abdukadir OBUL
2011-01-01
The authors take all isomorphism classes of indecomposable representations as new generators, and obtain all skew-commutators between these generators by using the Ringel-Hall algebra method. Then they prove that the set of these skew-commutators is a Gr(o)bner-Shirshov basis for quantum group of type D4.
Felder's elliptic quantum group and elliptic hypergeometric series on the root system A_n
Rosengren, Hjalmar
2010-01-01
We introduce a generalization of elliptic 6j-symbols, which can be interpreted as matrix elements for intertwiners between corepresentations of Felder's elliptic quantum group. For special parameter values, they can be expressed in terms of multivariable elliptic hypergeometric series related to the root system A_n. As a consequence, we obtain new biorthogonality relations for such series.
Bicovariant differential geometry of the quantum group GL$_{q}$(3)
Aschieri, Paolo; Aschieri, Paolo; Castellani, Leonardo
1992-01-01
We construct a bicovariant differential calculus on the quantum group $GL_q(3)$, and discuss its restriction to $[SU(3) \\otimes U(1)]_q$. The $q$-algebra of Lie derivatives is found, as well as the Cartan-Maurer equations. All the quantities characterizing the non-commutative geometry of $GL_q(3)$ are given explicitly.
Part III, Free Actions of Compact Quantum Groups on C*-Algebras
Schwieger, Kay; Wagner, Stefan
2017-08-01
We study and classify free actions of compact quantum groups on unital C^*-algebras in terms of generalized factor systems. Moreover, we use these factor systems to show that all finite coverings of irrational rotation C^*-algebras are cleft.
Mezey, Paul G
2014-09-16
Conspectus Just as complete molecules have no boundaries and have "fuzzy" electron density clouds approaching zero density exponentially at large distances from the nearest nucleus, a physically justified choice for electron density fragments exhibits similar behavior. Whereas fuzzy electron densities, just as any fuzzy object, such as a thicker cloud on a foggy day, do not lend themselves to easy visualization, one may partially overcome this by using isocontours. Whereas a faithful representation of the complete fuzzy density would need infinitely many such isocontours, nevertheless, by choosing a selected few, one can still obtain a limited pictorial representation. Clearly, such images are of limited value, and one better relies on more complete mathematical representations, using, for example, density matrices of fuzzy fragment densities. A fuzzy density fragmentation can be obtained in an exactly additive way, using the output from any of the common quantum chemical computational techniques, such as Hartree-Fock, MP2, and various density functional approaches. Such "fuzzy" electron density fragments properly represented have proven to be useful in a rather wide range of applications, for example, (a) using them as additive building blocks leading to efficient linear scaling macromolecular quantum chemistry computational techniques, (b) the study of quantum chemical functional groups, (c) using approximate fuzzy fragment information as allowed by the holographic electron density theorem, (d) the study of correlations between local shape and activity, including through-bond and through-space components of interactions between parts of molecules and relations between local molecular shape and substituent effects, (e) using them as tools of density matrix extrapolation in conformational changes, (f) physically valid averaging and statistical distribution of several local electron densities of common stoichiometry, useful in electron density databank mining, for
A coassociative C$*$-quantum group with non-integral dimensions
Böhm, G
1995-01-01
By weakening the counit and antipode axioms of a C*-Hopf algebra and allowing for the coassociative coproduct to be non-unital we obtain a quantum group, that we call a weak C*-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. This amounts to generalizing the Baaj-Skandalis multiplicative unitaries to multipicative partial isometries. Every weak C*-Hopf algebra has a dual which is again a weak C*-Hopf algebra. An explicit example is presented with Lee-Yang fusion rules. We shortly discuss applications to amalgamated crossed products, doubles, and quantum chains.
Conformal invariance and renormalization group in quantum gravity near two dimensions
Aida, Toshiaki; Kitazawa, Yoshihisa; Kawai, Hikaru; Ninomiya, Masao
1994-09-01
We study quantum gravity in 2 + ɛ dimensions in such a way as to preserve the volume-preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the renormalization group flow to the Einstein theory at long distance. We emphasize that the consistent and macroscopic universes like our own can only exist for a matter central charge 0 effect and universes are found to bounce back from the big crunch. Our formulation may be viewed as a Ginzburg-Landau theory which can describe both the broken and the unbroken phase of quantum gravity and the phase transition between them.
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.
Yang, Guowu; Song, Xiaoyu; Perkowski, Marek
2011-01-01
We propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as Controlled-Square-Root-of-Not (i.e. Controlled-V). Our approach reduces the synthesis problem to multiple-valued optimization and uses group theory. We devise a novel technique that transforms the quantum logic synthesis problem from a multi-valued constrained optimization problem to a group permutation problem. The transformation enables us to utilize group theory to exploit the properties of the synthesis problem. Assuming a cost of one for each two-qubit gate, we found all reversible circuits with quantum costs of 4, 5, 6, etc, and give another algorithm to realize these reversible circuits with quantum gates.
Quantum group approach to a soluble vertex model with generalized ice-rule
Cire, L S; Cire, L Sow
1995-01-01
Using the representation of the quantum group SL_q(2) by the Weyl ope\\-ra\\-tors of the canonical commutation relations in quantum mechanics, we construct and solve a new vertex model on a square lattice. Random variables on horizontal bonds are Ising variables, and those on the vertical bonds take half positive integer values. The vertices is subjected to a genera\\-li\\-zed form of the so-called ``ice-rule'', its property are studied in details and its free energy calculated with the method of quantum inverse scattering. Remarkably in analogy with the usual six-vertex model, there exists a ``Free-Fermion'' limit with a novel rich operator structure. The existing algebraic structure suggests a possible connection with a lattice neutral plasma of charges, via the Fermion-Boson correspondence.
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.
First-order differential calculi over multi-braided quantum groups
Durdevic, M
1996-01-01
A differential calculus of the first order over multi-braided quantum groups is developed. In analogy with the standard theory, left/right-covariant and bicovariant differential structures are introduced and investigated. Furthermore, antipodally covariant calculi are studied. The concept of the *-structure on a multi-braided quantum group is formulated, and in particular the structure of left-covariant *-covariant calculi is analyzed. A special attention is given to differential calculi covariant with respect to the action of the associated braid system. In particular it is shown that the left/right braided-covariance appears as a consequence of the left/right-covariance relative to the group action. Braided counterparts of all basic results of the standard theory are found.
Clifford groups of quantum gates, BN-pairs and smooth cubic surfaces
Energy Technology Data Exchange (ETDEWEB)
Planat, Michel [Institut FEMTO-ST, CNRS, 32 Avenue de l' Observatoire, F-25044 Besancon (France); Sole, Patrick [CNRS I3S, Les Algorithmes, Euclide B, 2000 route des Lucioles, BP 121, 06903 Sophia Antipolis (France)
2009-01-30
The recent proposal (Planat and Kibler 2008 arXiv:0807.3650 [quant-ph]) of representing Clifford quantum gates in terms of unitary reflections is revisited. In this communication, the geometry of a Clifford group G is expressed as a BN-pair, i.e. a pair of subgroups B and N that generate G, is such that intersection H = B intersection N is normal in G, the group W = N/H is a Coxeter group and two extra axioms are satisfied by the double cosets acting on B. The BN-pair used in this decomposition relies on the swap and match gates already introduced for classically simulating quantum circuits (Jozsa and Miyake 2008 arXiv:0804.4050 [quant-ph]). The two- and three-qubit cases are related to the configuration with 27 lines on a smooth cubic surface. (fast track communication)
Quantum groups as generalized gauge symmetries in WZNW models. Part II. The quantized model
Hadjiivanov, L.; Furlan, P.
2017-07-01
This is the second part of a paper dealing with the "internal" (gauge) symmetry of the Wess-Zumino-Novikov-Witten (WZNW) model on a compact Lie group G. It contains a systematic exposition, for G = SU( n), of the canonical quantization based on the study of the classical model (performed in the first part) following the quantum group symmetric approach first advocated by L.D. Faddeev and collaborators. The internal symmetry of the quantized model is carried by the chiral WZNW zero modes satisfying quadratic exchange relations and an n-linear determinant condition. For generic values of the deformation parameter the Fock representation of the zero modes' algebra gives rise to a model space of U q ( sl( n)). The relevant root of unity case is studied in detail for n = 2 when a "restricted" (finite dimensional) quotient quantum group is shown to appear in a natural way. The module structure of the zero modes' Fock space provides a specific duality with the solutions of the Knizhnik-Zamolodchikov equation for the four point functions of primary fields suggesting the existence of an extended state space of logarithmic CFT type. Combining left and right zero modes (i.e., returning to the 2 D model), the rational CFT structure shows up in a setting reminiscent to covariant quantization of gauge theories in which the restricted quantum group plays the role of a generalized gauge symmetry.
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.
Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity
Bonanno, A
2002-01-01
Homogeneous and isotropic cosmologies of the Planck era before the classical Einstein equations become valid are studied taking quantum gravitational effects into account. The cosmological evolution equations are renormalization group improved by including the scale dependence of Newton's constant and of the cosmological constant as it is given by the flow equation of the effective average action for gravity. It is argued that the Planck regime can be treated reliably in this framework because gravity is found to become asymptotically free at short distances. The epoch immediately after the initial singularity of the Universe is described by an attractor solution of the improved equations which is a direct manifestation of an ultraviolet attractive renormalization group fixed point. It is shown that quantum gravity effects in the very early Universe might provide a resolution to the horizon and flatness problem of standard cosmology, and could generate a scale-free spectrum of primordial density fluctuations.
Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\\hat{sl_N})$
Kojima, Takeo
2011-01-01
We construct two classes of infinitely many commuting operators associated with the elliptic quantum group $U_{q,p}(\\hat{sl_N})$. We call one of them the integral of motion ${\\cal G}_m$, $(m \\in {\\mathbb N})$ and the other the boundary transfer matrix $T_B(z)$, $(z \\in {\\mathbb C})$. The integral of motion ${\\cal G}_m$ is related to elliptic deformation of the $N$-th KdV theory. The boundary transfer matrix $T_B(z)$ is related to the boundary $U_{q,p}(\\hat{sl_N})$ face model. We diagonalize the boundary transfer matrix $T_B(z)$ by using the free field realization of the elliptic quantum group, however diagonalization of the integral of motion ${\\cal G}_m$ is open problem even for the simplest case $U_{q,p}(\\hat{sl_2})$.
Extended renormalizations group analysis for quantum gravity and Newton's gravitational constant
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S. [Department of Physics, University of Alexandria (Egypt); Donghua University, Shanghai (China)], E-mail: Chaossf@aol.com
2008-02-15
The conventional renormalization groups as applied in SU(5) GUT are adapted to the transfinite simplictic arithmetic of E-infinity theory. The resulting simple formalism yielded the exact quantum gravity inverse coupling for non-super symmetric and super symmetric unifications alike. Subsequently by means of analogy supported by Witten's T-duality and black hole theory an accurate estimation of Newton's constant of gravity is derived from what is basically the same formalism.
Dorofeeva, O. V.; Ryzhova, O. N.; Moiseeva, N. F.
2008-06-01
The enthalpies of formation, entropies, and heat capacities of 95 organophosphorus derivatives calculated by nonempirical quantum-chemical methods were used to develop the additive method for estimating the thermodynamic properties of these compounds. 86 group contribution values were obtained for estimating the thermodynamic properties of diverse organic derivatives of phosphorus in the oxidation states 3 and 5 (three-and four-coordinate phosphorus atoms).
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.
Non-compact groups, tensor operators and applications to quantum gravity
Sellaroli, Giuseppe
2016-01-01
This work focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. First, the mathematical theory of tensor operators for a Lie group is recast in a new way which is used to generalise the Wigner-Eckart theorem to non-compact groups. The result relies on the knowledge of the recoupling theory between finite-dimensional and infinite-dimensional irreducible representations of the group; here the previously unconsidered cases of the 3D and 4D Lorentz groups are investigated in detail. As an application, the Wigner-Eckart theorem is used to generalise the Jordan-Schwinger representation of SU(2) to both groups, for all representation classes. Next, the results obtained for the 3D Lorentz group are applied to (2+1) Lorentzian loop quantum gravity to develop an analogue of the well-known spinorial approach used in the Euclidean case. Tensor operators are used to construct observables and to generalise the Hamiltonian constraint introduced by Bonzom and Liv...
Laser field induced optical gain in a group III-V quantum wire
Saravanan, Subramanian; Peter, Amalorpavam John; Lee, Chang Woo
2016-08-01
Effect of intense high frequency laser field on the electronic and optical properties of heavy hole exciton in an InAsP/InP quantum well wire is investigated taking into consideration of the spatial confinement. Laser field induced exciton binding energies, optical band gap, oscillator strength and the optical gain in the InAs0.8P0.2/InP quantum well wire are studied. The variational formulism is applied to find the respective energies. The laser field induced optical properties are studied. The optical gain as a function of photon energy, in the InAs0.8P0.2/InP quantum wire, is obtained in the presence of intense laser field. The compact density matrix method is employed to obtain the optical gain. The results show that the 1.55 μm wavelength for the fibre optic telecommunication applications is achieved for 45 Å wire radius in the absence of laser field intensity whereas the 1.55 μm wavelength is obtained for 40 Å if the amplitude of the laser field amplitude parameter is 50 Å. The characterizing wavelength for telecommunication network is optimized when the intense laser field is applied for the system. It is hoped that the obtained optical gain in the group III-V narrow quantum wire can be applied for fabricating laser sources for achieving the preferred telecommunication wavelength.
Energy Technology Data Exchange (ETDEWEB)
Lee, Hyun-Jung [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Institut fuer Physik, Universitaet Augsburg, D-86135 Augsburg (Germany); Bulla, Ralf [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Institut fuer Physik, Universitaet Augsburg, D-86135 Augsburg (Germany); Vojta, Matthias [Institut fuer Theorie der Kondensierten Materie, Universitaet Karlsruhe, D-76128 Karlsruhe (Germany)
2005-11-02
The numerical renormalization group method is used to investigate zero-temperature phase transitions in quantum impurity systems, in particular in the particle-hole symmetric soft-gap Anderson model. The model displays two stable phases whose fixed points can be built up of non-interacting single-particle states. In contrast, the quantum phase transitions turn out to be described by interacting fixed points, and their excitations cannot be described in terms of free particles. We show that the structure of the many-body spectrum of these critical fixed points can be understood using renormalized perturbation theory close to certain values of the bath exponents which play the role of critical dimensions. Contact is made with perturbative renormalization group calculations for the soft-gap Anderson and Kondo models. A complete description of the quantum critical many-particle spectra is achieved using suitable marginal operators; technically this can be understood as epsilon-expansion for full many-body spectra.
Lee, Hyun-Jung; Bulla, Ralf; Vojta, Matthias
2005-11-01
The numerical renormalization group method is used to investigate zero-temperature phase transitions in quantum impurity systems, in particular in the particle-hole symmetric soft-gap Anderson model. The model displays two stable phases whose fixed points can be built up of non-interacting single-particle states. In contrast, the quantum phase transitions turn out to be described by interacting fixed points, and their excitations cannot be described in terms of free particles. We show that the structure of the many-body spectrum of these critical fixed points can be understood using renormalized perturbation theory close to certain values of the bath exponents which play the role of critical dimensions. Contact is made with perturbative renormalization group calculations for the soft-gap Anderson and Kondo models. A complete description of the quantum critical many-particle spectra is achieved using suitable marginal operators; technically this can be understood as epsilon-expansion for full many-body spectra.
González-Ruiz, A
1994-01-01
We consider integrable open-boundary conditions for the supersymmetric t-J model commuting with the number operator $n$ and $S^{z}$. We find four families, each one depending on two arbitrary parameters. The associated eigenvalue problem is solved by generalizing the Nested Algebraic Bethe Ansatz of the quantum group invariant case (which is obtained as a special limit). For the quantum group invariant case the Bethe ansatz states are shown to be highest weights of $spl_{q}(2,1)$. We also discuss the relation between Sklyanin's method of constructing open boundary conditions and the one for the quantum group invariant case based on Markov traces.
The dual roles of functional groups in the photoluminescence of graphene quantum dots.
Wang, Shujun; Cole, Ivan S; Zhao, Dongyuan; Li, Qin
2016-04-14
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 sp(3) 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 sp(3) 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.
Conformal invariance and renormalization group in quantum gravity near two dimensions
Aida, T; Kawai, H; Ninomiya, M
1994-01-01
We study quantum gravity in 2+\\epsilon dimensions in such a way to preserve the volume preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the renormalization group flow to Einstein theory at long distance. We emphasize that the consistent and macroscopic universes like our own can only exist for matter central charge 0
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.
Vol, E D
2012-01-01
In present paper we propose the consistent statistical approach which appropriate for a number of models describing both behavior of biological populations and various social groups interacting with each other.The approach proposed based on the ideas of quantum theory of open systems (QTOS) and allows one to account explicitly both discreteness of a system variables and their fluctuations near mean values.Therefore this approach can be applied also for the description of small populations where standard dynamical methods are failed. We study in detail three typical models of interaction between populations and groups: 1) antagonistic struggle between two populations 2) cooperation (or, more precisely, obligatory mutualism) between two species 3) the formation of coalition between two feeble groups in their conflict with third one that is more powerful . The models considered in a sense are mutually complementary and include the most types of interaction between populations and groups. Besides this method can ...
Quasi-quantum groups from Kalb-Ramond fields and magnetic amplitudes for strings on orbifolds
Jureit, J H
2006-01-01
We present the general form of the operators that lift the group action on the twisted sectors of a bosonic string on an orbifold ${\\cal M}/G$, in the presence of a Kalb-Ramond field strength $H$. These operators turn out to generate the quasi-quantum group $D_{\\omega}[G]$, introduced in the context of orbifold conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche. The 3-cocycle $\\omega$ entering in the definition of $D_{\\omega}[G]$ is related to $H$ by a series of cohomological equations in a tricomplex combining de Rham, Cech and group coboundaries. We construct magnetic amplitudes for the twisted sectors and show that $\\omega=1$ arises as a consistency condition for the orbifold theory. Finally, we recover discrete torsion as an ambiguity in the lift of the group action to twisted sectors, in accordance with previous results presented by E. Sharpe.
Indian Academy of Sciences (India)
Debashish Goswami
2015-02-01
Let be one of the classical compact, simple, centre-less, connected Lie groups of rank with a maximal torus , the Lie algebra $\\mathcal{G}$ and let $\\{E_{i},F_{i},H_{i},i=1,\\ldots,n\\}$ be tha standard set of generators corresponding to a basis of the root system. Consider the adjoint-orbit space $M=\\{\\text{Ad}_{g}(H_{1}), g\\in G\\}$, identified with the homogeneous space / where $L=\\{g\\in G : \\text{Ad}_{g}(H_{1})=H_{1}\\}$. We prove that the coordinate functions $f_{i}(g):=_{i}(\\text{Ad}_{g}(H_{1}))$, $i=1,\\ldots,n$, where $\\{_{1},\\ldots,_{n}\\}$ is basis of $\\mathcal{G}'$ are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on $C(M)$ such that the action leaves invariant the linear span of the above coordinate functions. As a corollary, it is also shown that any compact quantum group having a faithful action on the noncommutative manifold obtained by Rieffel deformation of satisfying a similar `linearity' condition must be a Rieffel-Wang type deformation of some compact group.
Coherent states, quantum gravity, and the Born- Oppenheimer approximation. II. Compact Lie groups
Stottmeister, Alexander; Thiemann, Thomas
2016-07-01
In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall "coherent state" transform for compact Lie groups G, which we prove for G = U(1)n and support by numerical evidence for G = SU(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups G. But, as Weyl and Berezin quantisation for ℝ2d are intimately related by heat kernel evolution, it is natural to ask whether a similar connection exists for compact Lie groups as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann-Hall transform, can serve as basis of the former.
Smith, Alexander R. H.; Piani, Marco; Mann, Robert B.
2016-07-01
Quantum communication without a shared reference frame or the construction of a relational quantum theory requires the notion of a quantum reference frame. We analyze aspects of quantum reference frames associated with noncompact groups, specifically, the group of spatial translations and Galilean boosts. We begin by demonstrating how the usually employed group average, used to dispense of the notion of an external reference frame, leads to unphysical states when applied to reference frames associated with noncompact groups. However, we show that this average does lead naturally to a reduced state on the relative degrees of freedom of a system, which was previously considered by Angelo et al. [J. Phys. A: Math. Theor. 44, 145304 (2011), 10.1088/1751-8113/44/14/145304]. We then study in detail the informational properties of this reduced state for systems of two and three particles in Gaussian states.
Kondo quantum dot coupled to ferromagnetic leads: Numerical renormalization group study
Sindel, M.; Borda, L.; Martinek, J.; Bulla, R.; König, J.; Schön, G.; Maekawa, S.; von Delft, J.
2007-07-01
We systematically study the influence of ferromagnetic leads on the Kondo resonance in a quantum dot tuned to the local moment regime. We employ Wilson’s numerical renormalization group method, extended to handle leads with a spin asymmetric density of states, to identify the effects of (i) a finite spin polarization in the leads (at the Fermi surface), (ii) a Stoner splitting in the bands (governed by the band edges), and (iii) an arbitrary shape of the lead density of states. For a generic lead density of states, the quantum dot favors being occupied by a particular spin species due to exchange interaction with ferromagnetic leads, leading to suppression and splitting of the Kondo resonance. The application of a magnetic field can compensate this asymmetry, restoring the Kondo effect. We study both the gate voltage dependence (for a fixed band structure in the leads) and the spin polarization dependence (for fixed gate voltage) of this compensation field for various types of bands. Interestingly, we find that the full recovery of the Kondo resonance of a quantum dot in the presence of leads with an energy-dependent density of states is possible not only by an appropriately tuned external magnetic field but also via an appropriately tuned gate voltage. For flat bands, simple formulas for the splitting of the local level as a function of the spin polarization and gate voltage are given.
Relational evolution of effectively interacting group field theory quantum gravity condensates
Pithis, Andreas G. A.; Sakellariadou, Mairi
2017-03-01
We study the impact of effective interactions onto relationally evolving group field theory (GFT) condensates based on real-valued fields. In a first step we show that a free condensate configuration in an isotropic restriction settles dynamically into a low-spin configuration of the quantum geometry. This goes hand in hand with the accelerated and exponential expansion of its volume, as well as the vanishing of its relative uncertainty which suggests the classicalization of the quantum geometry. The dynamics of the emergent space can then be given in terms of the classical Friedmann equations. In contrast to models based on complex-valued fields, solutions avoiding the singularity problem can only be found if the initial conditions are appropriately chosen. We then turn to the analysis of the influence of effective interactions on the dynamics by studying in particular the Thomas-Fermi regime. In this context, at the cost of fine-tuning, an epoch of inflationary expansion of quantum geometric origin can be implemented. Finally, and for the first time, we study anisotropic GFT condensate configurations and show that such systems tend to isotropize quickly as the value of the relational clock grows. This paves the way to a more systematic investigation of anisotropies in the context of GFT condensate cosmology.
Baratin, Aristide
2011-01-01
Using the non-commutative metric formulation of group field theories (GFT), we define a model of 4-dimensional quantum gravity as a constrained BF theory, without Immirzi parameter, encoding the quantum simplicial geometry of any triangulation used to define its quantum amplitudes. This involves a generalization of the usual GFT framework, where the usual field variables, associated to the four triangles of a tetrahedron, are supplemented by an S^3 vector playing the role of the normal to the tetrahedron. This leads naturally to projected spin network states. We give both a simplicial path integral and a spin foam formulation of the Feynman amplitudes, which correspond to a variant of the Barrett-Crane amplitudes. We then re-examin the arguments against the Barrett-Crane model(s), in light of our construction. We argue that it can still be considered a plausible quantization of 4d gravity, and that further work is needed to either confirm or refute its validity.
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
Group theory in quantum mechanics an introduction to its present usage
Heine, Volker
2007-01-01
Geared toward research students in physics and chemistry, this text introduces the three main uses of group theory in quantum mechanics: (1) to label energy levels and the corresponding eigenstates; (2) to discuss qualitatively the splitting of energy levels, starting from an approximate Hamiltonian and adding correction terms; and (3) to aid in the evaluation of matrix elements of all kinds.""The theme,"" states author Volker Heine, ""is to show how all this is achieved by considering the symmetry properties of the Hamiltonian and the way in which these symmetries are reflected in the wave fu
Real-space renormalization group method for quantum 1/2 spins on the pyrochlore lattice.
Garcia-Adeva, Angel J
2014-04-02
A simple phenomenological real-space renormalization group method for quantum Heisenberg spins with nearest and next nearest neighbour interactions on a pyrochlore lattice is presented. Assuming a scaling law for the order parameter of two clusters of different sizes, a set of coupled equations that gives the fixed points of the renormalization group transformation and, thus, the critical temperatures and ordered phases of the system is found. The particular case of spins 1/2 is studied in detail. Furthermore, to simplify the mathematical details, from all the possible phases arising from the renormalization group transformation, only those phases in which the magnetic lattice is commensurate with a subdivision of the crystal lattice into four interlocked face-centred cubic sublattices are considered. These correspond to a quantum spin liquid, ferromagnetic order, or non-collinear order in which the total magnetic moment of a tetrahedral unit is zero. The corresponding phase diagram is constructed and the differences with respect to the classical model are analysed. It is found that this method reproduces fairly well the phase diagram of the pyrochlore lattice under the aforementioned constraints.
Gessner, Manuel; Breuer, Heinz-Peter
2013-04-01
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of complex open quantum systems, employing arguments from ensemble theory. We further generalize these results to arbitrary eigenvalue distributions, allowing a detailed comparison of typical regular and chaotic systems with the help of concepts from random matrix theory. To illustrate the physical relevance and the general applicability of our results we present a series of examples related to the fields of open quantum systems and nonequilibrium quantum thermodynamics. These include the effect of initial correlations, the average quantum dynamical maps, the generic dynamics of system-environment pure state entanglement and, finally, the equilibration of generic open and closed quantum systems.
Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic
2010-01-01
We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu2O2]2+ core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu2O2]2+.
Invariant q-Schrödinger equation from homogeneous spaces of the 2-dim Euclidean quantum group
Bonechi, F; Giachetti, R; Sorace, E; Tarlini, M; Bonechi, F; Ciccoli, N; Giachetti, R; Sorace, E; Tarlini, M
1994-01-01
After a preliminary review of the definition and the general properties of the homogeneous spaces of quantum groups, the quantum hyperboloid (qH) and the quantum plane (qP) are determined as homogeneous spaces of F_q(E(2)). The canonical action of E_q(2) is used to define a natural q-analog of the free Schrodinger equation, that is studied in the momentum and angular momentum bases. In the first case the eigenfunctions are factorized in terms of products of two q-exponentials. In the second case we determine the eigenstates of the unitary representation, which, in the (qP) case, are given in terms Hahn-Exton functions. Introducing the universal T-matrix for E_q(2) we prove that the Hahn-Exton q-Bessel functions are also obtained as matrix elements of T, giving thus the correct extension to quantum groups of well known methods in harmonic analysis.
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.
Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire
Directory of Open Access Journals (Sweden)
Norman J. M. Horing
2017-06-01
Full Text Available This work is concerned with the derivation of the Green’s function for Landau-quantized carriers in the Group-VI dichalcogenides. In the spatially homogeneous case, the Green’s function is separated into a Peierls phase factor and a translationally invariant part which is determined in a closed form integral representation involving only elementary functions. The latter is expanded in an eigenfunction series of Laguerre polynomials. These results for the retarded Green’s function are presented in both position and momentum representations, and yet another closed form representation is derived in circular coordinates in terms of the Bessel wave function of the second kind (not to be confused with the Bessel function. The case of a quantum wire is also addressed, representing the quantum wire in terms of a model one-dimensional δ(x-potential profile. This retarded Green’s function for propagation directly along the wire is determined exactly in terms of the corresponding Green’s function for the system without the δ(x-potential, and the Landau quantized eigenenergy dispersion relation is examined. The thermodynamic Green’s function for the dichalcogenide carriers in a normal magnetic field is formulated here in terms of its spectral weight, and its solution is presented in a momentum/integral representation involving only elementary functions, which is subsequently expanded in Laguerre eigenfunctions and presented in both momentum and position representations.
Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire
Horing, Norman J. M.
2017-06-01
This work is concerned with the derivation of the Green's function for Landau-quantized carriers in the Group-VI dichalcogenides. In the spatially homogeneous case, the Green's function is separated into a Peierls phase factor and a translationally invariant part which is determined in a closed form integral representation involving only elementary functions. The latter is expanded in an eigenfunction series of Laguerre polynomials. These results for the retarded Green's function are presented in both position and momentum representations, and yet another closed form representation is derived in circular coordinates in terms of the Bessel wave function of the second kind (not to be confused with the Bessel function). The case of a quantum wire is also addressed, representing the quantum wire in terms of a model one-dimensional δ (x ) -potential profile. This retarded Green's function for propagation directly along the wire is determined exactly in terms of the corresponding Green's function for the system without the δ (x ) -potential, and the Landau quantized eigenenergy dispersion relation is examined. The thermodynamic Green's function for the dichalcogenide carriers in a normal magnetic field is formulated here in terms of its spectral weight, and its solution is presented in a momentum/integral representation involving only elementary functions, which is subsequently expanded in Laguerre eigenfunctions and presented in both momentum and position representations.
The Quantum Group Structure of 2D Gravity and Minimal Models; 2, The Genus-Zero Chiral Bootstrap
Cremmer, E; Roussel, J F; Gervais, Jean-Loup
1994-01-01
The F and B matrices associated with Virasoro null vectors are derived in closed form by making use of the operator-approach suggested by the Liouville theory, where the quantum-group symmetry is explicit. It is found that the entries of the fusing and braiding matrices are not simply equal to quantum-group symbols, but involve additional coupling constants whose derivation is one aim of the present work. Our explicit formulae are new, to our knowledge, in spite of the numerous studies of this problem. The relationship between the quantum-group-invariant (of IRF type) and quantum-group-covariant (of vertex type) chiral operator-algebras is fully clarified, and connected with the transition to the shadow world for quantum-group symbols. The corresponding 3-j-symbol dressing is shown to reduce to the simpler transformation of Babelon and one of the author (J.-L. G.) in a suitable infinite limit defined by analytic continuation. The above two types of operators are found to coincide when applied to states with L...
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
Hieida, Yasuhiro; Okunishi, Kouichi; Akutsu, Yasuhiro
1997-02-01
The product-wave-function renormalization group method, a new numerical renormalization group scheme proposed recently, is applied to one-dimensional quantum spin chains in a magnetic field. We find the zero-temperature magnetization curve of the spin chains, which excellently agrees with the exact solution in the whole range of the field.
The functional renormalization group for interacting quantum systems with spin-orbit interaction
Energy Technology Data Exchange (ETDEWEB)
Grap, Stephan Michael [RWTH Aachen (Germany). Inst. fuer Theorie der Statistischen Physik
2013-07-15
We studied the influence of spin-orbit interaction (SOI) in interacting low dimensional quantum systems at zero temperature within the framework of the functional renormalization group (fRG). Among the several types of spin-orbit interaction the so-called Rashba spin-orbit interaction is especially intriguing for future spintronic applications as it may be tuned via external electric fields. We investigated its effect on the low energy physics of an interacting quantum wire in an applied Zeeman field which is modeled as a generalization of the extended Hubbard model. To this end we performed a renormalization group study of the two particle interaction, including the SOI and the Zeeman field exactly on the single particle level. Considering the resulting two band model, we formulated the RG equations for the two particle vertex keeping the full band structure as well as the non trivial momentum dependence of the low energy two particle scattering processes. In order to solve these equations numerically we defined criteria that allowed us to classify whether a given set of initial conditions flows towards the strongly coupled regime. We found regions in the models parameter space where a weak coupling method as the fRG is applicable and it is possible to calculate additional quantities of interest. Furthermore we analyzed the effect of the Rashba SOI on the properties of an interacting multi level quantum dot coupled to two semi in nite leads. Of special interest was the interplay with a Zeeman field and its orientation with respect to the SOI term. We found a renormalization of the spin-orbit energy which is an experimental quantity used to asses SOI effects in transport measurements, as well as renormalized effective g factors used to describe the Zeeman field dependence. In particular in asymmetrically coupled systems the large parameter space allows for rich physics which we studied by means of the linear conductance obtained via the generalized Landauer
Chishtie, F A
2002-01-01
Pade approximants (PA) have been widely applied in practically all areas of physics. This thesis focuses on developing PA as tools for both perturbative and non- perturbative quantum field theory (QFT). In perturbative QFT, we systematically estimate higher (unknown) loop terms via the asymptotic formula devised by Samuel et al. This algorithm, generally denoted as the asymptotic Pade approximation procedure (APAP), has greatly enhanced scope when it is applied to renormalization-group-(RG-) invariant quantities. A presently-unknown higher-loop quantity can then be matched with the approximant over the entire momentum region of phenomenological interest. Furthermore, the predicted value of the RG coefficients can be compared with the RG-accessible coefficients (at the higher-loop order), allowing a clearer indication of the accuracy of the predicted RG-inaccessible term. This methodology is applied to hadronic Higgs decay rates (H → bb¯ and H → gg, both within the Standard Model and...
Ohsaku, T; Yamaki, D; Yamaguchi, K
2002-01-01
For studying the group theoretical classification of the solutions of the density functional theory in relativistic framework, we propose quantum electrodynamical density-matrix functional theory (QED-DMFT). QED-DMFT gives the energy as a functional of a local one-body $4\\times4$ matrix $Q(x)\\equiv -$, where $\\psi$ and $\\bar{\\psi}$ are 4-component Dirac field and its Dirac conjugate, respectively. We examine some characters of QED-DMFT. After these preparations, by using Q(x), we classify the solutions of QED-DMFT under O(3) rotation, time reversal and spatial inversion. The behavior of Q(x) under nonrelativistic and ultrarelativistic limits are also presented. Finally, we give plans for several extensions and applications of QED-DMFT.
The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group
Fan, H; Shi, K J; Yue, R H; Zhao, S Y; Fan, Heng; Hou, Bo-Yu; Shi, Kang-Jie; Yue, Rui-Hong; Zhao, Shao-You
2003-01-01
In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation of the $A_{n-1}$ series elliptic quantum group given by Felder and Varchenko. The explicit dependence of elements of $L$-matrices on spectral parameter $z$ are given. They are of five different forms (A(1-4) and B). The algebra for the coefficients (which do not depend on $z$) are given. The algebra of form A is proved to be trivial, while that of form B obey Yang-Baxter equation (YBE). We also give the PBW base and the centers for the algebra of form B.
Effective Gauge Group of Pure Loop Quantum Gravity is SO(3)
Chou, C H; Soo, C; Yu, H L; Chou, Chung-Hsien; Ling, Yi; Soo, Chopin; Yu, Hoi-Lai
2006-01-01
We argue that the effective gauge group for {\\it pure} four-dimensional loop quantum gravity(LQG) is SO(3) (or $SO(3,C)$) instead of SU(2) (or $SL(2,C)$). As a result, links in spin network states for pure LQG should be labeled by integer spins only, implying a modification of the spectra of area and volume operators where all half-integer spins allowed in previous discussions are now absent. Our observations resolve puzzling difficulties in matching the Bekenstein-Hawking entropy, and in fixing the Immirzi parameter from LQG calculations to the results from quasi-normal mode excitations of a Schwarzschild black hole. Moreover, in agreement with our conclusions, the results of both pure LQG and the supersymmetric extension of LQG can be made compatible, provided we accept $j_{min}=1$ for the former, and $j'_{min}=1/2$ for the latter.
Spin-Anisotropy Commensurable Chains Quantum Group Symmetries and N=2 SUSY
Berkovich, A; Sierra, G
1994-01-01
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 depends on the N-parity. For the N even case at the commensurable point, S-matrices factorize into N=2 supersymmetric Sine-Gordon matrix and an RSOS piece. The physics of the N odd case is rather different. Here, the supersymmetry does not manifest itself and the bootstrap hypothesis fails. Away from the commensurable point, we find an unusual behaviour. The magnetization of our chains depends on the sign of the external magnetic field.
The Power of Strong Fourier Sampling: Quantum Algorithms for Affine Groups and Hidden Shifts
Moore, Cristopher; Russell, A; Schulman, L J; Moore, Cristopher; Rockmore, Daniel; Russell, Alexander; Schulman, Leonard J.
2005-01-01
Many quantum algorithms, including Shor's celebrated factoring and discrete log algorithms, proceed by reduction to a Hidden Subgroup problem, in which an unknown subgroup H of a group G must be determined from a uniform superposition on a left coset of H. These hidden subgroup problems are typically solved by Fourier sampling. When G is nonabelian, two important variants of Fourier sampling have been identified: the weak standard method, where only representation names are measured, and the strong standard method, where full measurement (i.e., the row and column of the representation, in a suitably chosen basis) occurs. It has remained open whether the strong standard method is indeed stronger. In this article, we settle this question in the affirmative. We show that hidden subgroups H of the q-hedral groups, i.e., semidirect products Z_q \\ltimes Z_p where q | (p-1), and in particular the affine groups A_p, can be information-theoretically reconstructed using the strong standard method. Moreover, if |H| = p/...
Optimization of TCR and heat transport in group-IV multiple-quantum-well microbolometers
Morea, Matthew; Gu, Kevin; Savikhin, Victoria; Fenrich, Colleen S.; Pop, Eric; Harris, James S.
2016-09-01
Group-IV semiconductors have the opportunity to have an equivalent or better temperature coefficient of resistance (TCR) than other microbolometer thermistor materials. By using multiple-quantum-well (MQW) structures, their TCR values can be optimized due to a confinement of carriers. Through two approaches - an activation energy approximation and a custom Monte Carlo transfer matrix method - we simulated this effect for a combination of Group-IV semiconductors and their alloys (e.g., SiGe and GeSn) to find the highest possible TCR, while keeping in mind the critical thicknesses of such layers in a MQW epitaxial stack. We calculated the TCR for a critical-thickness-limited Ge0.8Sn0.2/Ge MQW device to be about -1.9 %/K. Although this TCR is lower than similar SiGe/Si MQW thermistors, GeSn offers possible advantages in terms of fabricating suspended devices with its interesting etch-stop properties shown in previous literature. Furthermore, using finite element modeling of heat transport, we looked at another key bolometer parameter: the thermal time constant. The dimensions of a suspended Ge microbolometer's supporting legs were fine-tuned for a target response time of 5 ms, incorporating estimations for the size effects of the nanowire-like legs on thermal conductivity.
Burgess, C P
2001-01-01
We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers satisfying Fermi statistics (or those related to fermions by the action of the group), the resulting group is known to imply many, if not all, of the remarkable features of Quantum Hall systems. For conductors with boson charge carriers (modulo group transformations) a different group is predicted, implying equally striking implications for the conductivities of these systems, including a super-universality of the critical exponents for conductor/insulator and superconductor/insulator transitions in two dimensions and a hierarchical structure, analogous to that of the quantum Hall effect but different in its details. Our derivation shows how this symmetry emerges at low energies, depending only weakly on the details of dynamics of the underlying systems.
Gosson, Maurice A. de
2012-01-01
Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level set...
The Hidden Quantum Group of the 8-vertex Free Fermion Model q-Clifford Algebras
Cuerno, R; López, E; Sierra, G
1993-01-01
We prove in this paper that the elliptic $R$--matrix of the eight vertex free fermion model is the intertwiner $R$--matrix of a quantum deformed Clifford--Hopf algebra. This algebra is constructed by affinization of a quantum Hopf deformation of the Clifford algebra.
A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry
Sharma, Sandeep
2014-01-01
We extend the spin-adapted density matrix renormalization group (DMRG) algorithm of McCulloch and Gulacsi [Europhys. Lett.57, 852 (2002)] to quantum chemical Hamiltonians. This involves two key modifications to the non-spin-adapted DMRG algorithm: the use of a quasi-density matrix to ensure that the renormalised DMRG states are eigenvalues of $S^2$ , and the use of the Wigner-Eckart theorem to greatly reduce the overall storage and computational cost. We argue that the advantages of the spin-adapted DMRG algorithm are greatest for low spin states. Consequently, we also implement the singlet-embedding strategy of Nishino et al [Phys. Rev. E61, 3199 (2000)] which allows us to target high spin states as a component of a mixed system which is overall held in a singlet state. We evaluate our algorithm on benchmark calculations on the Fe$_2$S$_2$ and Cr$_2$ transition metal systems. By calculating the full spin ladder of Fe$_2$S$_2$ , we show that the spin-adapted DMRG algorithm can target very closely spaced spin ...
Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group
Vian, Federica
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 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 ...
Quantum group spin nets: refinement limit and relation to spin foams
Dittrich, Bianca; Steinhaus, Sebastian
2013-01-01
So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups $\\text{SU}(2)_k$ and examine their effective continuum dynamics via tensor network renormalization. In the refinement limit of this coarse graining procedure, we find a vast non-trivial fixed point structure beyond the degenerate and the $BF$ phase. In comparison to previous work, we use fixed point intertwiners, inspired by Reisenberger's construction principle [1] and the recent work [2], as the initial parametrization. In this new parametrization fine tuning is not required in order to flow to these new fixed points. Encouragingly, each fixed point has an associated extended phase, which allows for the study of phase transitions in the future. Finally we also present an interpretation of spin nets in terms of melonic spin foams. The coarse graining flow of spin nets can thus be interpreted as describing the...
Forced gradings in integral quasi-hereditary algebras with applications to quantum groups
Parshall, Brian
2012-01-01
Let $\\sO$ be a discrete valuation ring with fraction field $K$ and residue field $k$. A quasi-hereditary algebra $\\wA$ over $\\sO$ provides a bridge between the representation theory of the quasi-hereditary algebra $\\wA_K:=K\\otimes \\wA$ over the field $K$ and the quasi-hereditary algebra $A_k:=k\\otimes_\\sO\\wA$ over $k$. In one important example, $\\wA_K$--mod is a full subcategory of the category of modules for a quantum enveloping algebra while $\\wA_k$--mod is a full subcategory of the category of modules for a reductive group in positive characteristic. This paper considers first the question of when the positively graded algebra $\\gr \\wA:= \\bigoplus_{n\\geq 0}(\\wA\\cap\\rad^n\\wA_K)/(\\wA\\cap\\rad^{n+1}\\wA_K)$ is quasi-hereditary. A main result gives sufficient conditions that $\\gr\\wA$ be quasi-hereditary. The main requirement is that each graded module $\\gr\\wDelta(\\lambda)$ arising from a $\\wA$-standard (Weyl) module $\\wDelta(\\lambda)$ have an irreducible head. An additional hypothesis requires that the graded al...
Chin, Alex W; Plenio, Martin B
2011-01-01
This chapter gives a self-contained review of the how standard open quantum system Hamiltonians can be mapped analytically onto representations in which the environments appear as one dimensional harmonic chains with nearest neighbour interactions. This mapping, carried out rigorously using orthogonal polynomial theory, then allows the full evolution of the system and environment to be simulated using time-adaptive density matrix renormalisation group methods. With the combination of these two techniques, numerically-exact results can be obtained for dissipative quantum systems in the presence of arbitrarily complex environmental spectral functions, and the correlations and processes in the environment which drive the effectively irreversible dynamics of the reduced state of the quantum system can be explored in real time. The chain representation also reveals a number of universal features of harmonic environments characterised by a spectral density which are discussed here.
Pérez-Mercader, J
1993-01-01
We define an entropy for a quantum field theory by combining quantum fluctuations, scaling and the maximum entropy concept. This entropy has different behavior in asymptotically free and non--asymptotically free theories. We find that the transition between the two regimes (from the asymptotically free to the non--asymptotically free) takes place via a continuous phase transition. For asymptotically free theories there exist regimes where the ``temperatures" are negative. In asymptotically free theories there exist maser--like states mostly in the infrared; furthermore, as one goes into the ultraviolet and more matter states contribute to quantum processes, the quantum field system can shed entropy and cause the formation of thermodynamically stable {\\it entropy--ordered} states. It is shown how the known heavier quarks can be thus described.
Free q-Schrödinger equation from homogeneous spaces of the 2-dim Euclidean quantum group
Bonechi, F.; Ciccoli, N.; Giachetti, R.; Sorace, E.; Tarlini, M.
1996-01-01
After a preliminary review of the definition and the general properties of the homogeneous spaces of quantum groups, the quantum hyperboloid qH and the quantum plane qP are determined as homogeneous spaces of F q ( E(2)). The canonical action of E q (2) is used to define a natural q-analog of the free Schrödinger equation, that is studied in the momentum and angular momentum bases. In the first case the eigenfunctions are factorized in terms of products of two q-exponentials. In the second case we determine the eigenstates of the unitary representation, which, in the qP case, are given in terms of Hahn-Exton functions. Introducing the universal T-matrix for E q (2) we prove that the Hahn-Exton as well as Jackson q-Bessel functions are also obtained as matrix elements of T, thus giving the correct extension to quantum groups of well known methods in harmonic analysis.
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.)
Distillation Protocols for Mixed States of Multilevel Qubits and the Quantum Renormalization Group
Martín-Delgado, M A
2003-01-01
We study several properties of distillation protocols to purify multilevel qubit states (qudits) when applied to a certain family of initial mixed bipartite states. We find that it is possible to use qudits states to increase the stability region obtained with the flow equations to distill qubits. In particular, for qutrits we get the phase diagram of the distillation process with a rich structure of fixed points. We investigate the large-$D$ limit of qudits protocols and find an analytical solution in the continuum limit. The general solution of the distillation recursion relations is presented in an appendix. We stress the notion of weight amplification for distillation protocols as opposed to the quantum amplitude amplification that appears in the Grover algorithm. Likewise, we investigate the relations between quantum distillation and quantum renormalization processes.
Blood group antigen studies using CdTe quantum dots and flow cytometry
Directory of Open Access Journals (Sweden)
Cabral Filho PE
2015-07-01
Full Text Available Paulo E Cabral Filho,1 Maria IA Pereira,1 Heloise P Fernandes,2 Andre A de Thomaz,3 Carlos L Cesar,3 Beate S Santos,4 Maria L Barjas-Castro,2 Adriana Fontes1 1Departamento de Biofísica e Radiobiologia, Universidade Federal de Pernambuco, Recife, Pernambuco, 2Centro de Hematologia e Hemoterapia, Universidade Estadual de Campinas, Instituto Nacional de Ciência e Tecnologia do Sangue, Campinas, São Paulo, 3Departamento de Eletrônica Quântica, Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Campinas, São Paulo, 4Departamento de Ciências Farmacêuticas, Universidade Federal de Pernambuco, Recife, PE, Brazil Abstract: New methods of analysis involving semiconductor nanocrystals (quantum dots [QDs] as fluorescent probes have been highlighted in life science. QDs present some advantages when compared to organic dyes, such as size-tunable emission spectra, broad absorption bands, and principally exceptional resistance to photobleaching. Methods applying QDs can be simple, not laborious, and can present high sensibility, allowing biomolecule identification and quantification with high specificity. In this context, the aim of this work was to apply dual-color CdTe QDs to quantify red blood cell (RBC antigen expression on cell surface by flow cytometric analysis. QDs were conjugated to anti-A or anti-B monoclonal antibodies, as well as to the anti-H (Ulex europaeus I lectin, to investigate RBCs of A1, B, A1B, O, A2, and Aweak donors. Bioconjugates were capable of distinguishing the different expressions of RBC antigens, both by labeling efficiency and by flow cytometry histogram profile. Furthermore, results showed that RBCs from Aweak donors present fewer amounts of A antigens and higher amounts of H, when compared to A1 RBCs. In the A group, the amount of A antigens decreased as A1 > A3 > AX = Ael, while H antigens were AX = Ael > A1. Bioconjugates presented stability and remained active for at least 6 months. In conclusion
de Gosson, Maurice A
2011-01-01
Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level sets defined by Fermi for the purpose of representing geometrically quantum states.
Raman gain in a Boron based Group-III nitride quantum well
Narayana Moorthy, N.; John Peter, A.; Lee, Chang Woo
2014-06-01
Electron Raman scattering of a hydrogenic impurity is studied using exact diagonalization method in a BxGa1-xN/BN coupled quantum well. Intersubband scattering rates, in a Boron based wide band gap GaN, are considered. BxGa1-xN semiconductor is taken as inner quantum well and BN material is taken as barrier material. The effect of quantum confinement on the differential cross section of Raman scattering, with and without the impurity, is obtained. The built-in internal electric field is included throughout the calculations. The third order susceptibility with the incident photon energy is calculated with and without doping impurity. The donor hydrogenic binding energy and its low lying excited states are computed taking into account the geometrical confinement. The binding energy is obtained for various impurity position and the Boron alloy content in BxGa1-xN quantum well. It is brought out that the geometrical confinement and built-in internal electric fields have great influence on the optical properties of the semiconductor.
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...
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...
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, 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....
Scalar quantum chromodynamics in two dimensions and parton model. [Scalar quarks, SU(N) groups
Energy Technology Data Exchange (ETDEWEB)
Shei, S.S.; Tsao, H.S.
1977-05-01
The SU(N) scalar quantum chromodynamics in two space-time dimensions in the large N limit are studied. This is the model of color gauge fields interacting with scalar quarks. It is found that the consensual properties of the four dimensional QCD, i.e., the infrared slavery, quark confinement, the charmonium picture etc. are all realized. Moreover, the current in this model mimics nicely the behaviors of current in the four dimensional QCD, in contrast to the original model of 't Hooft.
Zhao, Jiang; Yu, Yue; Yang, Xiaolong; Yan, Xiaogang; Zhang, Huiming; Xu, Xianbin; Zhou, Guijiang; Wu, Zhaoxin; Ren, Yixia; Wong, Wai-Yeung
2015-11-11
A series of heteroleptic functional Ir(III) complexes bearing different fluorinated aromatic sulfonyl groups has been synthesized. Their photophysical features, electrochemical behaviors, and electroluminescent (EL) properties have been characterized in detail. These complexes emit intense yellow phosphorescence with exceptionally high quantum yields (ΦP > 0.9) at room temperature, and the emission maxima of these complexes can be finely tuned depending upon the number of the fluorine substituents on the pendant phenyl ring of the sulfonyl group. Furthermore, the electrochemical properties and electron injection/transporting (EI/ET) abilities of these Ir(III) phosphors can also be effectively tuned by the fluorinated aromatic sulfonyl group to furnish some desired characters for enhancing the EL performance. Hence, the maximum luminance efficiency (ηL) of 81.2 cd A(-1), corresponding to power efficiency (ηP) of 64.5 lm W(-1) and external quantum efficiency (ηext) of 19.3%, has been achieved, indicating the great potential of these novel phosphors in the field of organic light-emitting diodes (OLEDs). Furthermore, a clear picture has been drawn for the relationship between their optoelectronic properties and chemical structures. These results should provide important information for developing highly efficient phosphors.
Indian Academy of Sciences (India)
Siddhartha Sen
2002-08-01
A classical phase space with a suitable symplectic structure is constructed together with functions which have Poisson brackets algebraically identical to the Lie algebra structure of the Lie group SU(3). It is shown that in this phase space there are two spheres which intersect at one point. Such a system has a representation as an algebraic curve of the form $X^{3} +\\cdots = 0$ in $\\mathscr{C}^{3}$. The curve introduced is singular at the origin in the limit when the radii of the spheres go to zero. A direct connection between the Lie groups SU(3) and a singular curve in $\\mathscr{C}^{3}$ is thus established. The key step needed to do this was to treat the Lie group as a quantum system and determine its phase space.
Probing the small distance structure of canonical quantum gravity using the conformal group
Hooft, Gerard 't
2010-01-01
In canonical quantum gravity, the formal functional integral includes an integration over the local conformal factor, and we propose to perform the functional integral over this factor before doing any of the other functional integrals. By construction, the resulting effective theory would be expected to be conformally invariant and therefore finite. However, also the conformal integral itself diverges, and therefore the actual situation is more delicate. The effects of a renormalization counter term are considered, including the associated problem of unitarity violation, such as a Landau-like ghost. Adding (massive or massless) matter fields does not change the picture; to confirm this, detailed calculations were necessary, and they are presented. Some alternative ideas are offered, including a more daring speculation, which is that no counter term should be allowed for at all. This has far-reaching and important consequences, which we discuss. A surprising picture emerges of quantized elementary particles i...
Account of Nonpolynomial SU(3)-Breaking Effects By Use of Quantum Groups As Flavor Symmetries
Gavrilik, A M
1998-01-01
Using instead of ordinary flavour symmetries SU(n_f) their corresponding quantum (q-deformed) analogs yields new baryon mass sum rules of extreme accuracy. We show, in the 3-flavour case, that such approach accounts for highly nonlinear (nonpolynomial) SU(3)-breaking effects both in the octet and decuplet baryon masses. A version of this approach is considered that involves q-covariant ingredients in the mass operator. The resulting new 'q-deformed' mass relation (q-MR) is simpler than previously derived q-MRs, but requires, for its empirical validity, a fitting to fix the value of the deformation parameter q. Well-known Gell-Mann--Okubo (GMO) octet mass sum rule is found to result not only from usual SU(3), but also from some exotic symmetry corresponding to the q=-1 (i.e., singular) limit of the q-algebra U_q(su_3).
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.
Jafarzadeh, Hossein; Sangachin, Elnaz Ahmadi; Asadpour, Seyyed Hossein
2015-07-01
In this paper, we propose a novel scheme for controlling the group velocity of transmitted and reflected pulse from defect medium doped with four-level InGaN/GaN quantum dot nanostructure. Quantum dot nanostructure is designed numerically by Schrödinger and Poisson equations which solve self consistently. By size control of quantum dot and external voltage, one can design a four-level quantum dot with appropriate energy levels which can be suitable for controlling the group velocity of pulse transmission and reflection from defect slab with terahertz signal field. It is found that in the presence and absence of terahertz signal field the behaviors of transmission and reflection pulses are completely different. Moreover, it is shown that for strong terahertz signal field, by changing the thickness of the slab, simultaneous peak and dip for transmission and reflection pulse are obtained.
Nakatani, Naoki; Chan, Garnet Kin-Lic
2013-04-07
We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.
Ercolessi, E; Morandi, G; Mukunda, N
2001-01-01
We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same method in the case of SU(3) we study the effect of degeneracies on geometric phases for three-level systems. This is shown to lead to a highly nontrivial generalization of the result for two-level systems in which degeneracy results in a "monopole" structure in parameter space. The rich structures that arise are related to the geometry of adjoint orbits in SU(3). The limiting case of a two-level degeneracy in a three-level system is shown to lead to the known monopole structure.
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
Sharatchandra, H S
2016-01-01
Real-Space renormalization group techniques are developed for tackling large curvature fluctuations in quantum gravity. Within cells of invariant volume $a^4$, only certain types of fluctuations are allowed. Normal coordinates are used to avoid redundancy of the degrees of freedom. The relevant integration measure is read off from the metric on metrics. All fluctuations in a group of cells are averaged over to get an effective action for the larger cell. In this paper the simplest type of fluctuations are kept. The measure is simply an integration over independent components of the curvature tensor at the center of each cell. Terms of higher order in $a$ are required for convergence in case of Einstein-Hilbert action. With only next order (in $a$) contribution to the action, there is no renormalization of Newton's or cosmological constants. The `massless Gaussian surface' in the renormalization group space is given by actions that have linear and quadratic terms in curvature and determines the evolution of co...
Arkan, Foroogh; Izadyar, Mohammad; Nakhaeipour, Ali
2015-12-01
In this work, ten porphyrin derivatives, including free-base zinc-metalised compounds were studied by varying the position of the carboxyl anchoring group and the alkyl substituents length on the remaining three phenyl rings with the aim of the cell efficiency investigation. Theoretical performances of the sensitisers in the dye-sensitised solar cell systems have been discussed by analysis of the optical absorption, the oxidised potential of ground and excited states, light-harvesting efficiency and electron injection efficiency. Due to lower symmetry of free-based porphyrins, they showed broader bands than zinc porphyrins. The second group sensitisers are better than the first one due to the smaller oxidation potential energy, higher open-circuit voltage and light-harvesting efficiency. The influence of long alkyl substituents on the photovoltaic parameters is not perceptible but ortho and meta positions of anchoring group modify the solar cell performance. Finally, some correlations between the quantum reactivity indices and photovoltaic parameters have obtained and discussed.
Quantum algebras for maximal motion groups of n-dimensional flat spaces
Ballesteros, A; Del Olmo, M A; Santander, M
1994-01-01
An embedding method to get q-deformations for the non-semisimple algebras generating the motion groups of N-dimensional flat spaces is presented. This method gives a global and simultaneous scheme of q-deformation for all iso(p,q) algebras and for those ones obtained from them by some Inönü-Wigner contractions, such as the N--dimensional Euclidean, Poincaré and Galilei algebras.
Group actions on C*-algebras, 3-cocycles and quantum field theory
Carey, A. L.; Grundling, H.; Raeburn, I.; Sutherland, C.
1995-03-01
We study group extensions Δ→Γ→Ω, where Γ acts on a C*-algebra A. Given a twisted covariant representation π, V of the pair A, Δ we construct 3-cocycles on Ω with values in the centre of the group generated by V(Δ). These 3-cocycles are obstructions to the existence of an extension of Ω by V(Δ) which acts on A compatibly with Γ. The main theorems of the paper introduce a subsidiary invariant Λ which classifies actions of Γ on V(Δ) and in terms of which a necessary and sufficient condition for the the cohomology class of the 3-cocycle to be non-trivial may be formulated. Examples are provided which show how non-trivial 3-cocycles may be realised. The framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories. We show how to interpret our results in that setting in two ways, one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups. In order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a Lie algebra version of the invariant Λ and the 3-cocycle.
The Density Matrix Renormalization Group applied to single-particle Quantum Mechanics
1999-01-01
A simplified version of White's Density Matrix Renormalization Group (DMRG) algorithm has been used to find the ground state of the free particle on a tight-binding lattice. We generalize this algorithm to treat the tight-binding particle in an arbitrary potential and to find excited states. We thereby solve a discretized version of the single-particle Schr\\"odinger equation, which we can then take to the continuum limit. This allows us to obtain very accurate results for the lowest energy le...
Effect of phase transition on quantum transport in group-IV two-dimensional U-shape device
Energy Technology Data Exchange (ETDEWEB)
Sadi, Mohammad Abdullah; Gupta, Gaurav, E-mail: a0089293@nus.edu.sg; Liang, Gengchiau [Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576 (Singapore)
2014-10-21
The effect of phase-transition from the quantum-spin-hall to the band-insulator phase on the transport through a three-terminal U-shape spin-separator has been computationally investigated via non-equilibrium green function formalism. Two-dimensional group-IV elements have been comprehensively appraised as the device material. The device separates the unpolarized current injected at the source-terminal into nearly 100% spin-polarized currents of the opposite polarities at the two drain terminals. The phase-transition activated by the electric-field orthogonal to the device is shown to extensively influence the current magnitude and its spin-polarization, and the effect is stronger for materials with smaller intrinsic spin-orbit coupling. Moreover, the device length and the area under field are shown to critically affect the device characteristics on phase change. It is shown that the same device can be operated as a spin-filter by inducing phase-transition selectively in the channel. The results are important for designing spin-devices from Group-IV monolayers.
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.
Quantum Operations as Quantum States
Arrighi, P; Arrighi, Pablo; Patricot, Christophe
2004-01-01
In this article we formalize the correspondence between quantum states and quantum operations, and harness its consequences. This correspondence was already implicit in Choi's proof of the operator sum representation of Completely Positive-preserving linear maps; we go further and show that all of the important theorems concerning quantum operations can be derived as simple corollaries of those concerning quantum states. As we do so the discussion first provides an elegant and original review of the main features of quantum operations. Next (in the second half of the paper) we search for more results to arise from the correspondence. Thus we propose a factorizability condition and an extremal trace-preservedness condition for quantum operations, give two novel Schmidt-type decompositions of bipartite pure states and two interesting composition laws for which the set of quantum operations and quantum states remain stable. The latter enables us to define a group structure upon the set of totally entangled state...
Mitchell, Andrew K.; Becker, Michael; Bulla, Ralf
2011-09-01
The existence of a length scale ξK˜1/TK (with TK the Kondo temperature) has long been predicted in quantum impurity systems. At low temperatures T≪TK, the standard interpretation is that a spin-(1)/(2) impurity is screened by a surrounding “Kondo cloud” of spatial extent ξK. We argue that renormalization group (RG) flow between any two fixed points (FPs) results in a characteristic length scale, observed in real space as a crossover between physical behavior typical of each FP. In the simplest example of the Anderson impurity model, three FPs arise, and we show that “free orbital,” “local moment,” and “strong coupling” regions of space can be identified at zero temperature. These regions are separated by two crossover length scales ξLM and ξK, with the latter diverging as the Kondo effect is destroyed on increasing temperature through TK. One implication is that moment formation occurs inside the “Kondo cloud”, while the screening process itself occurs on flowing to the strong coupling FP at distances ˜ξK. Generic aspects of the real-space physics are exemplified by the two-channel Kondo model, where ξK now separates local moment and overscreening clouds.
Gautam, Priyanka; Prakash, Om; Dani, R K; Singh, N K; Singh, Ranjan K
2014-11-11
1-Benzoyl-4-phenyl-3-thiosemicarbazide (H3bpt) was treated with acid - base in one sequence and base - acid in other sequence, both of which lead to ring formation of thiosemicarbazide group, giving N-phenyl-5-phenyl-1,3,4-thiadiazol-2-amine (Hppta) in the first case and 4,5-diphenyl-2,4-dihydro-1,2,4-triazole-3-thione (Hdptt) in the second case. The primary (H3bpt) as well as the resulting compounds (Hppta & Hdptt) has been characterized by elemental analyses, NMR, FTIR and Raman spectroscopic techniques. The quantum chemical calculations of the compounds are performed using DFT/B3LYP/6311G(d,p) method for geometry optimizations and also for prediction of the molecular properties. The cyclization is confirmed by disappearance of many bands belonging to the open chain subgroups of H3bpt such as; NH stretching, NH bending, CN stretching, NH puckering, CO stretching etc. The ring formation of 1-benzoyl-4-phenyl-3-thiosemicarbazide (H3bpt) has been further confirmed by the appearance of many bands belonging to the closed ring of thiosemicarbazide in the resulting compounds Hppta and Hdptt.
Quantum Permanents and Hafnians via Pfaffians
Jing, Naihuan; Zhang, Jian
2016-10-01
Quantum determinants and Pfaffians or permanents and Hafnians are introduced on the two-parameter quantum general linear group. Fundamental identities among quantum Pf, Hf, and det are proved in the general setting. We show that there are two special quantum algebras among the quantum groups, where the quantum Pfaffians have integral Laurent polynomials as coefficients. As a consequence, the quantum Hafnian is computed by a closely related quantum permanent and identical to the quantum Pfaffian on this special quantum algebra.
Rose, F.; Dupuis, N.
2017-01-01
Using a nonperturbative functional renormalization-group approach to the two-dimensional quantum O (N ) model, we compute the low-frequency limit ω →0 of the zero-temperature conductivity in the vicinity of the quantum critical point. Our results are obtained from a derivative expansion to second order of a scale-dependent effective action in the presence of an external (i.e., nondynamical) non-Abelian gauge field. While in the disordered phase the conductivity tensor σ (ω ) is diagonal, in the ordered phase it is defined, when N ≥3 , by two independent elements, σA(ω ) and σB(ω ) , respectively associated to SO (N ) rotations which do and do not change the direction of the order parameter. For N =2 , the conductivity in the ordered phase reduces to a single component σA(ω ) . We show that limω→0σ (ω ,δ ) σA(ω ,-δ ) /σq2 is a universal number, which we compute as a function of N (δ measures the distance to the quantum critical point, q is the charge, and σq=q2/h the quantum of conductance). On the other hand we argue that the ratio σB(ω →0 ) /σq is universal in the whole ordered phase, independent of N and, when N →∞ , equal to the universal conductivity σ*/σq at the quantum critical point.
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...
Langari, A; Pollmann, F; Siahatgar, M
2013-10-09
We study the phase diagram of the anisotropic spin-1 Heisenberg chain with single ion anisotropy (D) using a ground-state fidelity approach. The ground-state fidelity and its corresponding susceptibility are calculated within the quantum renormalization group scheme where we obtained the renormalization of fidelity preventing calculation of the ground state. Using this approach, the phase boundaries between the antiferromagnetic Néel, Haldane and large-D phases are obtained for the whole phase diagram, which justifies the application of quantum renormalization group to trace the symmetry-protected topological phases. In addition, we present numerical exact diagonalization (Lanczos) results in which we employ a recently introduced non-local order parameter to locate the transition from Haldane to large-D phase accurately.
On the controllability of a quantum system for the Morse potential with a compact group SU(2)
Energy Technology Data Exchange (ETDEWEB)
Dong Shihai; Tang Yu; Sun Guohua
2003-12-29
The controllability of a quantum system for the Morse potential with the bound states are investigated. The ladder operators are constructed directly from the wave functions with the factorization method and associated to an su(2) algebra. This quantum system with the discrete bound states can be strongly completely controlled, i.e., the eigenstates can be guided by the external field to approach arbitrarily close to a selected target state at any chosen time, which can be theoretically realized by the actions of the ladder operators on the ground state.
Quantum correlations and measurements
Energy Technology Data Exchange (ETDEWEB)
Sperling, Jan
2015-07-16
The present thesis is a state of the art report on the characterization techniques and measurement strategies to verify quantum correlations. I mainly focus on research which has been performed in the theoretical quantum optics group at the University of Rostock during the last few years. The results include theoretical findings and analysis of experimental studies of radiation fields. We investigate the verification of quantum properties, the quantification of these quantum effects, and the characterization of quantum optical detector systems.
Schmitt, Sebastian; Anders, Frithjof B.
2010-04-01
The quantum transport through nanoscale junctions is governed by the charging energy U of the device. We employ the recently developed scattering-states numerical renormalization-group approach to open quantum systems to study nonequilibrium Green’s functions and current-voltage characteristics of such junctions for small and intermediate values of U . We establish the accuracy of the approach by a comparison with diagrammatic Kadanoff-Baym-Keldysh results which become exact in the weak-coupling limit U→0 . We demonstrate the limits of the diagrammatic expansions at intermediate values of the charging energy. While the numerical renormalization-group approach correctly predicts only one single, universal low-energy scale at zero bias voltage, some diagrammatic expansions yield two different low-energy scales for the magnetic and the charge fluctuations. At large voltages, however, the self-consistent second Born as well as the GW approximation reproduce the scattering-states renormalization-group spectral functions for symmetric junctions while for asymmetric junctions the voltage-dependent redistribution of spectral weight differs significantly in the different approaches. The second-order perturbation theory does not capture the correct single-particle dynamics at large bias and violates current conservation for asymmetric junctions.
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...
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.
Santana, Juan A.; Krogel, Jaron T.; Kent, Paul R. C.; Reboredo, Fernando A.
2016-05-01
We have applied the diffusion quantum Monte Carlo (DMC) method to calculate the cohesive energy and the structural parameters of the binary oxides CaO, SrO, BaO, Sc2O3, Y2O3, and La2O3. The aim of our calculations is to systematically quantify the accuracy of the DMC method to study this type of metal oxides. The DMC results were compared with local, semi-local, and hybrid Density Functional Theory (DFT) approximations as well as with experimental measurements. The DMC method yields cohesive energies for these oxides with a mean absolute deviation from experimental measurements of 0.18(2) eV, while with local, semi-local, and hybrid DFT approximations, the deviation is 3.06, 0.94, and 1.23 eV, respectively. For lattice constants, the mean absolute deviations in DMC, local, semi-local, and hybrid DFT approximations are 0.017(1), 0.07, 0.05, and 0.04 Å, respectively. DMC is a highly accurate method, outperforming the DFT approximations in describing the cohesive energies and structural parameters of these binary oxides.
Rose, Félix
2016-01-01
Using a nonperturbative functional renormalization-group approach to the two-dimensional quantum O($N$) model, we compute the low-frequency limit $\\omega\\to 0$ of the zero-temperature conductivity in the vicinity of the quantum critical point. Our results are obtained from a derivative expansion to second order of a scale-dependent effective action in the presence of an external (i.e., non-dynamical) non-Abelian gauge field. While in the disordered phase the conductivity tensor $\\sigma(\\omega)$ is diagonal, in the ordered phase it is defined, when $N\\geq 3$, by two independent elements, $\\sigma_{\\rm A}(\\omega)$ and $\\sigma_{\\rm B}(\\omega)$, respectively associated to SO($N$) rotations which do and do not change the direction of the order parameter. For $N=2$, the conductivity in the ordered phase reduces to a single component $\\sigma_{\\rm A}(\\omega)$. We show that $\\lim_{\\omega\\to 0}\\sigma(\\omega,\\delta)\\sigma_{\\rm A}(\\omega,-\\delta)/\\sigma_q^2$ is a universal number which we compute as a function of $N$ ($\\d...
Quantum entanglement and symmetry
Energy Technology Data Exchange (ETDEWEB)
Chruscinski, D; Kossakowski, A [Institute of Physics, Nicolaus Copernicus University, Grudziadzka 5/7, 87-100 Torun (Poland)
2007-11-15
One of the main problem in Quantum Information Theory is to test whether a given state of a composite quantum system is entangled or separable. It turns out that within a class of states invariant under the action of the symmetry group this problem considerably simplifies. We analyze multipartite invariant states and the corresponding symmetric quantum channels.
Quantum entanglement and symmetry
Chruściński, D.; Kossakowski, A.
2007-11-01
One of the main problem in Quantum Information Theory is to test whether a given state of a composite quantum system is entangled or separable. It turns out that within a class of states invariant under the action of the symmetry group this problem considerably simplifies. We analyze multipartite invariant states and the corresponding symmetric quantum channels.
Institute of Scientific and Technical Information of China (English)
2008-01-01
After giving a bird's view of some existing quantum programming languages,this paper reports the recent results made by the quantum computation group of the State Key Laboratory for Novel Software Technology and the Department of Computer Science and Technology at Nanjing University,i.e.,the quantum programming languages NDQJava,NDQFP and their processing systems.
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
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 ...
Svenson, Eric Johan
Participants on the Invincible America Assembly in Fairfield, Iowa, and neighboring Maharishi Vedic City, Iowa, practicing Maharishi Transcendental Meditation(TM) (TM) and the TM-Sidhi(TM) programs in large groups, submitted written experiences that they had had during, and in some cases shortly after, their daily practice of the TM and TM-Sidhi programs. Participants were instructed to include in their written experiences only what they observed and to leave out interpretation and analysis. These experiences were then read by the author and compared with principles and phenomena of modern physics, particularly with quantum theory, astrophysics, quantum cosmology, and string theory as well as defining characteristics of higher states of consciousness as described by Maharishi Vedic Science. In all cases, particular principles or phenomena of physics and qualities of higher states of consciousness appeared qualitatively quite similar to the content of the given experience. These experiences are presented in an Appendix, in which the corresponding principles and phenomena of physics are also presented. These physics "commentaries" on the experiences were written largely in layman's terms, without equations, and, in nearly every case, with clear reference to the corresponding sections of the experiences to which a given principle appears to relate. An abundance of similarities were apparent between the subjective experiences during meditation and principles of modern physics. A theoretic framework for understanding these rich similarities may begin with Maharishi's theory of higher states of consciousness provided herein. We conclude that the consistency and richness of detail found in these abundant similarities warrants the further pursuit and development of such a framework.
Experimental investigation of quantum Simpson's paradox
Li, Yu-Long; Tang, Jian-Shun; Wang, Yi-Tao; Wu, Yu-Chun; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can; Yu, Ying; Li, Mi-Feng; Zha, Guo-Wei; Ni, Hai-Qiao; Niu, Zhi-Chuan
2013-07-01
The well-known Simpson's paradox, or Yule-Simpson (YS) effect, is often encountered in social-science and medical-science statistics. It occurs when the correlations present in different groups are reversed if the groups are combined. Simpson's paradox also exists in quantum measurements. In this Brief Report, we experimentally realized two analogous effects: the quantum-classical YS effect and the quantum-quantum YS effect in the quantum-dot system. We also compared the probability of obtaining those two effects under identical quantum measurements and found that the quantum-quantum YS effect is more likely to occur than the quantum-classical YS effect.
Directory of Open Access Journals (Sweden)
Prashant Anil Patil
2012-04-01
Full Text Available This paper gives the detailed information about Quantum computer, and difference between quantum computer and traditional computers, the basis of Quantum computers which are slightly similar but still different from traditional computer. Many research groups are working towards the highly technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. Quantum computer is very much use full for computation purpose in field of Science and Research. Large amount of data and information will be computed, processing, storing, retrieving, transmitting and displaying information in less time with that much of accuracy which is not provided by traditional computers.
Entanglement, quantum phase transitions and quantum algorithms
Orus, R
2006-01-01
The work that we present in this thesis tries to be at the crossover of quantum information science, quantum many-body physics, and quantum field theory. We use tools from these three fields to analyze problems that arise in the interdisciplinary intersection. More concretely, in Chapter 1 we consider the irreversibility of renormalization group flows from a quantum information perspective by using majorization theory and conformal field theory. In Chapter 2 we compute the entanglement of a single copy of a bipartite quantum system for a variety of models by using techniques from conformal field theory and Toeplitz matrices. The entanglement entropy of the so-called Lipkin-Meshkov-Glick model is computed in Chapter 3, showing analogies with that of (1+1)-dimensional quantum systems. In Chapter 4 we apply the ideas of scaling of quantum correlations in quantum phase transitions to the study of quantum algorithms, focusing on Shor's factorization algorithm and quantum algorithms by adiabatic evolution solving a...
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.
Geometrical aspects of quantum spaces
Energy Technology Data Exchange (ETDEWEB)
Ho, P.M. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group
1996-05-11
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S{sub 1}{sup 2} and the quantum complex projective space CP{sub q}(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S{sub q}{sup 2} and CP{sub q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP{sub q}(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given.
Generic Quantum Fourier Transforms
Moore, Cristopher; Russell, A; Moore, Cristopher; Rockmore, Daniel; Russell, Alexander
2003-01-01
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the separation of variables technique that has been so successful in the study of classical Fourier transform computations. Specifically, this framework applies the existence of computable Bratteli diagrams, adapted factorizations, and Gel'fand-Tsetlin bases to offer efficient quantum circuits for the QFT over a wide variety a finite Abelian and non-Abelian groups, including all group families for which efficient QFTs are currently known and many new group families. Moreover, the method gives rise to the first subexponential-size quantum circuits for the QFT over the linear groups GL_k(q), SL_k(q), and the finite groups of Lie type, for any fixed prime power q.
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.
Yard, J; Devetak, I; Yard, Jon; Hayden, Patrick; Devetak, Igor
2006-01-01
We analyze quantum broadcast channels, which are quantum channels with a single sender and many receivers. Focusing on channels with two receivers for simplicity, we generalize a number of results from the network Shannon theory literature which give the rates at which two senders can receive a common message, while a personalized one is sent to one of them. Our first collection of results applies to channels with a classical input and quantum outputs. The second class of theorems we prove concern sending a common classical message over a quantum broadcast channel, while sending quantum information to one of the receivers. The third group of results we obtain concern communication over an isometry, giving the rates at quantum information can be sent to one receiver, while common quantum information is sent to both, in the sense that tripartite GHZ entanglement is established. For each scenario, we provide an additivity proof for an appropriate class of channels, yielding single-letter characterizations of the...
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...
Virtually Abelian quantum walks
Mauro D'Ariano, Giacomo; Erba, Marco; Perinotti, Paolo; Tosini, Alessandro
2017-01-01
We study discrete-time quantum walks on Cayley graphs of non-Abelian groups, focusing on the easiest case of virtually Abelian groups. We present a technique to reduce the quantum walk to an equivalent one on an Abelian group with coin system having larger dimension. This method allows one to extend the notion of wave-vector to the virtually Abelian case and study analytically the walk dynamics. We apply the technique in the case of two quantum walks on virtually Abelian groups with planar Cayley graphs, finding the exact solution in terms of dispersion relation.
Microwave Quantum Illumination
2016-07-29
Df Introduction .– Entanglement is the foundation of many quantum information protocols [1–3], but it is easily de- stroyed by environmental noise that...1Institute for Quantum Information , RWTH Aachen University, 52056 Aachen, Germany 2Quantum Information Processing Group, Raytheon BBN Technologies...entanglement, theory showed that the QI system will significantly outperform a clas- sical (coherent-state) system of the same transmitted energy [5–7
Quantum broadcast communication
Institute of Scientific and Technical Information of China (English)
Wang Jian; Zhang Quan; Tang Chao-Jing
2007-01-01
Broadcast encryption allows the sender to securely distribute his/her secret to a dynamically changing group of users over a broadcast channel. In this paper, we just take account of a simple broadcast communication task in quantum scenario, in which the central party broadcasts his secret to multi-receiver via quantum channel. We present three quantum broadcast communication schemes. The first scheme utilizes entanglement swapping and GreenbergerHorne-Zeilinger state to fulfil a task that the central party broadcasts the secret to a group of receivers who share a group key with him. In the second scheme, based on dense coding, the central party broadcasts the secret to multi-receiver,each of which shares an authentication key with him. The third scheme is a quantum broadcast communication scheme with quantum encryption, in which the central party can broadcast the secret to any subset of the legal receivers.
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.
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.
Quantum classifying spaces and universal quantum characteristic classes
Durdevic, M
1996-01-01
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced and analyzed. Interrelations with the abstract algebraic theory of quantum characteristic classes are discussed. Various non-equivalent approaches to defining universal characteristic classes are outlined.
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.
Controllability of Quantum Systems
Schirmer, S G; Solomon, A I
2003-01-01
An overview and synthesis of results and criteria for open-loop controllability of Hamiltonian quantum systems obtained using Lie group and Lie algebra techniques is presented. Negative results for open-loop controllability of dissipative systems are discussed, and the superiority of closed-loop (feedback) control for quantum systems is established.
Multiparameter quantum supergroups
Hazewinkel, M.
1996-01-01
This paper is supplementary to my paper ``Multiparameter Quantum Groups and Multiparameter $R$-Matrices'', [5]. Its main purpose is to point out that among the single block solutions of the Yang-Baxter equation given in [5] there occurs an ${n+m choose 2 +1$ parameter quantum deformation of the supe
Quantum walks on Cayley graphs
Energy Technology Data Exchange (ETDEWEB)
Lopez Acevedo, O [Laboratoire de Physique Theorique et Modelisation, Universite de Cergy-Pontoise, 2 Avenue Adolphe Chauvin 95302 Cergy Pontoise Cedex (France); Institut fuer Mathematik und Informatik, Ernst-Moritz-Arndt-Universitaet, Friedrich-Ludwig-Jahn Str.15a, 17487 Greifswald (Germany); Gobron, T [Laboratoire de Physique Theorique et Modelisation, Universite de Cergy-Pontoise, 2 Avenue Adolphe Chauvin 95302 Cergy Pontoise Cedex (France)
2006-01-20
We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert space and consider various classes of graphs on which the structure of quantum walks may differ. We completely characterize quantum walks on free groups and present partial results on more general cases. Some examples are given including a family of quantum walks on the hypercube involving a Clifford algebra.
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.
Chang, Mou-Hsiung
2015-01-01
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...
Steane, A M
1998-01-01
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory. It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, the review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the EPR experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory, and, arguably, quantum from classical physics. Basic quantum information ideas are described, including key distribution, teleportation, data compression, quantum error correction, the universal quantum computer and qua...
Quantum Mechanics in the Infrared
Radicevic, Djordje
2016-01-01
This paper presents an algebraic formulation of the renormalization group flow in quantum mechanics on flat target spaces. For any interacting quantum mechanical theory, the fixed point of this flow is a theory of classical probability, not a different effective quantum mechanics. Each energy eigenstate of the UV Hamiltonian flows to a probability distribution whose entropy is a natural diagnostic of quantum ergodicity of the original state. These conclusions are supported by various examples worked out in detail.
Energy Technology Data Exchange (ETDEWEB)
Lee, Ko-Hsin; Thomas, Kevin; Gocalinska, Agnieszka; Manganaro, Marina; Corbett, Brian [Tyndall National Institute, University College Cork, Lee Maltings, Prospect Row, Cork (Ireland); Pelucchi, Emanuele; Peters, Frank H. [Tyndall National Institute, University College Cork, Lee Maltings, Prospect Row, Cork (Ireland); Department of Physics, University College Cork, Cork (Ireland)
2012-11-01
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 after the intermixing process involving the encapsulation of thin SiN{sub x} dielectric films on the surface followed by rapid thermal annealing. In addition to the annealing temperature, we report that the band gap shift can be also enhanced by increasing the CS level in the SQW. For instance, at an annealing temperature of 850 Degree-Sign C, the photoluminescence blue shift is found to reach more than 110 nm for the sample with 1.2%-CS SQW, but only 35 nm with 0.4%-CS SQW. We expect that this relatively larger atomic compositional gradient of In (and Ga) between the compressively strained quantum well and the barrier can facilitate the atomic interdiffusion and it thus leads to the larger band gap shift.
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.
2016-01-01
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. PMID:27695198
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 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.
2016-11-01
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.
Quantum critical points in quantum impurity systems
Energy Technology Data Exchange (ETDEWEB)
Lee, Hyun Jung [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universitaet Augsburg (Germany); Bulla, Ralf [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universitaet Augsburg (Germany)]. E-mail: bulla@cpfs.mpg.de
2005-04-30
The numerical renormalization group method is used to investigate zero-temperature phase transitions in quantum impurity systems, in particular in the soft-gap Anderson model, where an impurity couples to a non-trivial fermionic bath. In this case, zero-temperature phase transitions occur between two different phases whose fixed points can be built up of non-interacting single-particle states. However, the quantum critical point cannot be described by non-interacting fermionic or bosonic excitations.
Quantum critical points in quantum impurity systems
Lee, Hyun Jung; Bulla, Ralf
2005-04-01
The numerical renormalization group method is used to investigate zero-temperature phase transitions in quantum impurity systems, in particular in the soft-gap Anderson model, where an impurity couples to a non-trivial fermionic bath. In this case, zero-temperature phase transitions occur between two different phases whose fixed points can be built up of non-interacting single-particle states. However, the quantum critical point cannot be described by non-interacting fermionic or bosonic excitations.
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.
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 Kaluza-Klein Compactification
Sochichiu, C.
1999-01-01
Kaluza--Klein compactification in quantum field theory is analysed from the perturbation theory viewpoint. Renormalisation group analysis for compactification size dependence of the coupling constant is proposed.
Kisil, Vladimir V.
2000-01-01
We describe an $p$-mechanical (see funct-an/9405002 and quant-ph/9610016) brackets which generate quantum (commutator) and classic (Poisson) brackets in corresponding representations of the Heisenberg group. We \\emph{do not} use any kind of semiclassic approximation or limiting procedures for $\\hbar \\to 0$. Harmonic oscillator considered within the approach. Keywords: Classic and quantum mechanics, Hamilton and Heisenberg equations, Poisson brackets, commutator, Heisenberg group.
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [California Institute of Technology, Pasadena, California 91125 (United States)
2013-06-15
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
Roberts, Jenny R; Antonini, James M.; Porter, Dale W.; Chapman, Rebecca S.; Scabilloni, James F.; Young, Shih-Houng; Schwegler-Berry, Diane; CASTRANOVA, VINCENT; Mercer, Robert R.
2013-01-01
Background The potential use of quantum dots (QD) in biomedical applications, as well as in other systems that take advantage of their unique physiochemical properties, has led to concern regarding their toxicity, potential systemic distribution, and biopersistence. In addition, little is known about workplace exposure to QD in research, manufacturing, or medical settings. The goal of the present study was to assess pulmonary toxicity, clearance, and biodistribution of QD with different funct...
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
Wu, L A; Wu, Lian-Ao; Lidar, Daniel
2005-01-01
Quantum computation and communication offer unprecedented advantages compared to classical information processing. Currently, quantum communication is moving from laboratory prototypes into real-life applications. When quantum communication networks become more widespread it is likely that they will be subject to attacks by hackers, virus makers, and other malicious intruders. Here we introduce the concept of "quantum malware" to describe such human-made intrusions. We offer a simple solution for storage of quantum information in a manner which protects quantum networks from quantum malware.
Institute of Scientific and Technical Information of China (English)
李伟; 苏刚
2012-01-01
文章简述了数值重正化群方法的历史发展,包括威耳逊（Wilson）的数值重正化群算法,S.R.White的密度矩阵重正化群方法,以及近期迅速发展的处理强关联量子系统的几种张量网络态与张量网络算法.在此基础上,文章重点介绍了作者最近提出的用于研究量子多体系统热力学性质的线性张量重正化群方法,以及该方法在一维和二维量子系统中的应用.%We review the development of numerical renormalization group methods, including Wilson＇s numerical renormalization group , White＇s density matrix renormalization group, and several recent rapidly developing tensor network state-based algorithms. Among these, particular emphasis is laid on the linearized tensor renormalization group method, which was recently proposed to accurately calculate the thermo dynamic properties of quantum many-body lattice systems, and which may have broad applications in both one- and two-dimensional quantum systems.
Scarani, Valerio; Iblisdir, Sofyan; Gisin, Nicolas; Acin, Antonio
2005-01-01
The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases. These "quantum cloning machines" are important tools for studying a wide variety of tasks, e.g. state estimation and eavesdropping on quantum cryptography. This paper provides a comprehensive review of quantum cloning machines (both for discrete-dimensional an...
Quantum Public-Key Cryptosystem
Luo, Ming-Xing; Chen, Xiu-Bo; Yun, Deng; Yang, Yi-Xian
2012-03-01
Quantum one-way functions play a fundamental role in cryptography because of its necessity for the secure encryption schemes taking into account the quantum computer. In this paper our purpose is to establish a theoretical framework for a candidate of the quantum one-way functions and quantum trapdoor functions based on one-parameter unitary groups. The dynamics of parameterized unitary groups ensure the one-wayness and quantum undistinguishability in different levels, and the physical feasibility are derived from the simultaneous approximation of its infinitesimal generators. Moreover, these special functions are used to construct new cryptosystems-the quantum public-key cryptosystems for encrypting both the classical and quantum information.
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
Quantum CPU and Quantum Algorithm
Wang, An Min
1999-01-01
Making use of an universal quantum network -- QCPU proposed by me\\upcite{My1}, it is obtained that the whole quantum network which can implement some the known quantum algorithms including Deutsch algorithm, quantum Fourier transformation, Shor's algorithm and Grover's algorithm.
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…
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…
Pfeiffer, P.; Egusquiza, I. L.; di Ventra, M.; Sanz, M.; Solano, E.
2016-07-01
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.
Quantum phase transitions in constrained Bose systems
Bonnes, Lars
2011-01-01
This doctoral thesis studies low dimensional quantum systems that can be realized in recent cold atom experiments. From the viewpoint of quantum statistical mechanics, the main emphasis is on the detailed study of the different quantum and thermal phases and their transitions using numerical methods, such as quantum Monte Carlo and the Tensor Network Renormalization Group. The first part of this work deals with a lattice Boson model subject to strong three-body losses. In a quantum-Zeno li...
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.
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
DEFF Research Database (Denmark)
2007-01-01
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......-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...
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.
Intrinsic Time Quantum Geometrodynamics
Ita, Eyo Eyo; Yu, Hoi-Lai
2015-01-01
Quantum Geometrodynamics with intrinsic time development and momentric variables is presented. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together with its ground state and primordial quantum fluctuations. Cotton-York potential dominates at early times when the universe was small; the ground state naturally resolves Penrose's Weyl Curvature Hypothesis, and thermodynamic and gravitational `arrows of time' point in the same direction. Ricci scalar potential corresponding to Einstein's General Relativity emerges as a zero-point energy contribution. A new set of fundamental canonical commutation relations without Planck's constant emerges from the unification of Gravitation and Quantum Mechanics.
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.
Putz, Volkmar
2015-01-01
We consider ways of conceptualizing, rendering and perceiving quantum music, and quantum art in general. Thereby we give particular emphasis to its non-classical aspects, such as coherent superposition and entanglement.
Quantum walks on Cayley graphs
Acevedo, O L
2006-01-01
We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. Thus we consider quantum walks on a general basis and try to classify them as a preliminary step in the construction of new algorithms that could be devised in this way. In particular, we discuss the choice of the dimension of the local Hilbert space, and consider various classes of graphs on which the structure of quantum walks may differ. We characterize completely the quantum walks on free groups and present partial results on more general cases. Examples are given among which a family of quantum walks on the hypercube involving a Clifford Algebra.
Cheon, T
2004-01-01
We show that the U(2) family of point interactions on a line can be utilized to provide the U(2) family of qubit operations for quantum information processing. Qubits are realized as localized states in either side of the point interaction which represents a controllable gate. The manipulation of qubits proceeds in a manner analogous to the operation of an abacus. Keywords: quantum computation, quantum contact interaction, quantum wire
Esteban Guevara
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...
2008-01-01
Quantum Nanomechanics is the emerging field which pertains to the mechanical behavior of nanoscale systems in the quantum domain. Unlike the conventional studies of vibration of molecules and phonons in solids, quantum nanomechanics is defined as the quantum behavior of the entire mechanical structure, including all of its constituents--the atoms, the molecules, the ions, the electrons as well as other excitations. The relevant degrees of freedom of the system are described by macroscopic var...
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
Fehr, S.
2010-01-01
Quantum 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. This is in shar
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...
Difference equations of quantum current operators and quantum parafermion construction
Ding, J; Ding, Jintai; Feigin, Boris
1996-01-01
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we prove that, for the integrable modules of $U_q(\\hat x^\\pm(zq^{\\pm 2k})$ are vertex operators satisfying certain q-difference equations, and we derive the quantum parafermions of $U_q(\\hat {\\frak sl}(2))$.
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 Computing for Quantum Chemistry
2010-09-01
This three-year project consisted on the development and application of quantum computer algorithms for chemical applications. In particular, we developed algorithms for chemical reaction dynamics, electronic structure and protein folding. The first quantum computing for
Quantum memory in quantum cryptography
Mor, T
1999-01-01
[Shortened abstract:] This thesis investigates the importance of quantum memory in quantum cryptography, concentrating on quantum key distribution schemes. In the hands of an eavesdropper -- a quantum memory is a powerful tool, putting in question the security of quantum cryptography; Classical privacy amplification techniques, used to prove security against less powerful eavesdroppers, might not be effective when the eavesdropper can keep quantum states for a long time. In this work we suggest a possible direction for approaching this problem. We define strong attacks of this type, and show security against them, suggesting that quantum cryptography is secure. We start with a complete analysis regarding the information about a parity bit (since parity bits are used for privacy amplification). We use the results regarding the information on parity bits to prove security against very strong eavesdropping attacks, which uses quantum memories and all classical data (including error correction codes) to attack th...
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.
Quantum entanglement and quantum operation
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
It is a simple introduction to quantum entanglement and quantum operations. The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations. It includes remote state preparation by using any pure entangled states, nonlocal operation implementation using entangled states, entanglement capacity of two-qubit gates and two-qubit gates construction.
Horodecki, R; Horodecki, M; Horodecki, K; Horodecki, Ryszard; Horodecki, Pawel; Horodecki, Michal; Horodecki, Karol
2007-01-01
All our former experience with application of quantum theory seems to say: {\\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via ...
Weaver, Nik
2010-01-01
We define a "quantum relation" on a von Neumann algebra M \\subset B(H) to be a weak* closed operator bimodule over its commutant M'. Although this definition is framed in terms of a particular representation of M, it is effectively representation independent. Quantum relations on l^\\infty(X) exactly correspond to subsets of X^2, i.e., relations on X. There is also a good definition of a "measurable relation" on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, we can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and we can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. We are also able to intrinsically characterize the quantum relations on M in terms of families of projections in M \\otimes B(l^2).
Azpiroz, Jon M; Ugalde, Jesus M; Infante, Ivan
2014-01-14
In this work, we build a benchmark data set of geometrical parameters, vibrational normal modes, and low-lying excitation energies for MX quantum dots, with M = Cd, Zn, and X = S, Se, Te. The reference database has been constructed by ab initio resolution-of-identity second-order approximate coupled cluster RI-CC2/def2-TZVPP calculations on (MX)6 model molecules in the wurtzite structure. We have tested 26 exchange-correlation density functionals, ranging from local generalized gradient approximation (GGA) and hybrid GGA to meta-GGA, meta-hybrid, and long-range corrected. The best overall functional is the hybrid PBE0 that outperforms all other functionals, especially for excited state energies, which are of particular relevance for the systems studied here. Among the DFT methodologies with no Hartree-Fock exchange, the M06-L is the best one. Local GGA functionals usually provide satisfactory results for geometrical structures and vibrational frequencies but perform rather poorly for excitation energies. Regarding the CdSe cluster, we also present a test of several basis sets that include relativistic effects via effective core potentials (ECPs) or via the ZORA approximation. The best basis sets in terms of computational efficiency and accuracy are the SBKJC and def2-SV(P). The LANL2DZ basis set, commonly employed nowadays on these types of nanoclusters, performs very disappointingly. Finally, we also provide some suggestions on how to perform calculations on larger systems keeping a balance between computational load and accuracy.
Ryabitskii, Aleksey B.; Bricks, Julia L.; Kachkovskii, Aleksey D.; Chernega, Alexander N.; Vlasenko, Yurii G.
2010-10-01
Conformational features of unsymmetrical monomethine cyanine dye 2-[(2-butyl-1,3-dimethylcyclohepta[ c]pyrrol-6(2 H)-ylidene)methyl]-3-ethyl-1,3-benzothiazol-3-ium iodide-perchlorate have been investigated in solution by means of NMR spectroscopy and in the solid state by X-ray diffraction. The possibility of molecule conformational transformations was proved by scanning of potential energy surface along torsion angels. The corresponding energy barriers values have been calculated by means of DFT (B3LYP and M05-2X) methods. A comparison of structural parameters obtained by means of both methods was reported. The isomerization process was investigated by dynamic NMR spectroscopy. A comparison of 1H NMR spectra recorded in different solvents was performed. It was shown that in solution, intramolecular rotation around the bond С(6) аzaazulene-С methyne decelerated in NMR time scale took place. The data on dynamic behavior of dye molecules have been compared with the experimental X-ray data. Quantum-chemical calculation results are in agreement with the experimental data.
Abdalla, M. Sebawe; Khalil, E. M.; Obada, A. S.-F.
2017-01-01
In the present communication, we consider the problem of two quantum systems with the Kerr-like medium nonlinearity. The system is cast form of an interaction between two operators of the form su(1 , 1) Lie algebra and su(2) Lie algebra. We obtain the wave function via the evolution operator where we use the Heisenberg equations of motion to derive the constants of motion. We discuss the atomic inversion. It is found that the Kerr-like medium decreases the amplitude and increases the fluctuations. Also we consider different types of squeezing, it is shown that the entropy squeezing is pronounced in the second quadrature, but it shows a small amount in the first quadrature. For the variance squeezing, a small amount occurs in the presence of the Kerr-like medium. However, the normal squeezing occurs in the first quadrature where the squeezing is sensitive to both the Kerr-like medium parameter and the initial state. Furthermore, the degree of entanglement is examined through the linear entropy. It is shown that the function decreases besides rapid fluctuations. The correlation function displays nonclassical behavior in addition to an increase in the amplitude of the fluctuations.
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...
Quantum random number generation
Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Qi, Bing; Zhang, Zhen
2016-06-01
Quantum physics can be exploited to generate true random numbers, which have important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness—coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. On the basis of the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a high speed by properly modelling the devices. The second category is self-testing QRNG, in which verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category that provides a tradeoff between the trustworthiness on the device and the random number generation speed.
Quantum Games and Quantum Discord
Nawaz, Ahmad
2010-01-01
We quantize prisoners dilemma and chicken game by our generalized quantization scheme to explore the role of quantum discord in quantum games. In order to establish this connection we use Werner-like state as an initial state of the game. In this quantization scheme measurement can be performed in entangled as well as in product basis. For the measurement in entangled basis the dilemma in both the games can be resolved by separable states with non-zero quantum discord. Similarly for product basis measurement the payoffs are quantum mechanical only for nonzero values of quantum discord.
Spin Foam Models with Finite Groups
Directory of Open Access Journals (Sweden)
Benjamin Bahr
2013-01-01
Full Text Available Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.
Spin foam models with finite groups
Bahr, Benjamin; Ryan, James P
2011-01-01
Spin foam models, loop quantum gravity and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community we provide an introduction to some essential concepts in the loop quantum gravity, spin foam and group field theory approach and point out the many connections to lattice field theory and condensed matter systems.
Quantum state transfer through noisy quantum cellular automata
Avalle, Michele; Genoni, Marco G.; Serafini, Alessio
2015-05-01
We model the transport of an unknown quantum state on one dimensional qubit lattices by means of a quantum cellular automata (QCA) evolution. We do this by first introducing a class of discrete noisy dynamics, in the first excitation sector, in which a wide group of classical stochastic dynamics is embedded within the more general formalism of quantum operations. We then extend the Hilbert space of the system to accommodate a global vacuum state, thus allowing for the transport of initial on-site coherences besides excitations, and determine the dynamical constraints that define the class of noisy QCA in this subspace. We then study the transport performance through numerical simulations, showing that for some instances of the dynamics perfect quantum state transfer is attainable. Our approach provides one with a natural description of both unitary and open quantum evolutions, where the homogeneity and locality of interactions allow one to take into account several forms of quantum noise in a plausible scenario.
Quantum cellular automata and free quantum field theory
D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-02-01
In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.
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
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...
Arrighi, P
2003-01-01
Alice communicates with words drawn uniformly amongst $\\{\\ket{j}\\}_{j=1..n}$, the canonical orthonormal basis. Sometimes however Alice interleaves quantum decoys $\\{\\frac{\\ket{j}+i\\ket{k}}{\\sqrt{2}}\\}$ between her messages. Such pairwise superpositions of possible words cannot be distinguished from the message words. Thus as malevolent Eve observes the quantum channel, she runs the risk of damaging the superpositions (by causing a collapse). At the receiving end honest Bob, whom we assume is warned of the quantum decoys' distribution, checks upon their integrity with a measurement. The present work establishes, in the case of individual attacks, the tradeoff between Eve's information gain (her chances, if a message word was sent, of guessing which) and the disturbance she induces (Bob's chances, if a quantum decoy was sent, to detect tampering). Besides secure channel protocols, quantum decoys seem a powerful primitive for constructing n-dimensional quantum cryptographic applications. Moreover the methods emp...
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....
2010-03-04
efficient or less costly than their classical counterparts. A large-scale quantum computer is certainly an extremely ambi- tious goal, appearing to us...outperform the largest classical supercomputers in solving some specific problems important for data encryption. In the long term, another application...which the quantum computer depends, causing the quantum mechanically destructive process known as decoherence . Decoherence comes in several forms
Hughes, R J; Dyer, P L; Luther, G G; Morgan, G L; Schauer, M M; Hughes, Richard J; Dyer, P; Luther, G G; Morgan, G L; Schauer, M
1995-01-01
Quantum cryptography is a new method for secret communications offering the ultimate security assurance of the inviolability of a Law of Nature. In this paper we shall describe the theory of quantum cryptography, its potential relevance and the development of a prototype system at Los Alamos, which utilises the phenomenon of single-photon interference to perform quantum cryptography over an optical fiber communications link.
Factorization Method in Quantum Mechanics
Dong, Shi-Hai
2007-01-01
This Work introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the Reader’s disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this classic method are the supersymmetric quantum mechanics, shape invariant potentials and group theoretical approaches. It is no exaggeration to say that this method has become the milestone of these approaches. In fact the Author’s driving force has been his desire to provide a comprehensive review volume that includes some new and significant results about the factorization method in quantum mechanics since the literature is inundated with scattered articles in this field, and to pave the Reader’s way into ...
Network-Centric Quantum Communications
Hughes, Richard
2014-03-01
Single-photon quantum communications (QC) offers ``future-proof'' cryptographic security rooted in the laws of physics. Today's quantum-secured communications cannot be compromised by unanticipated future technological advances. But to date, QC has only existed in point-to-point instantiations that have limited ability to address the cyber security challenges of our increasingly networked world. In my talk I will describe a fundamentally new paradigm of network-centric quantum communications (NQC) that leverages the network to bring scalable, QC-based security to user groups that may have no direct user-to-user QC connectivity. With QC links only between each of N users and a trusted network node, NQC brings quantum security to N2 user pairs, and to multi-user groups. I will describe a novel integrated photonics quantum smartcard (``QKarD'') and its operation in a multi-node NQC test bed. The QKarDs are used to implement the quantum cryptographic protocols of quantum identification, quantum key distribution and quantum secret splitting. I will explain how these cryptographic primitives are used to provide key management for encryption, authentication, and non-repudiation for user-to-user communications. My talk will conclude with a description of a recent demonstration that QC can meet both the security and quality-of-service (latency) requirements for electric grid control commands and data. These requirements cannot be met simultaneously with present-day cryptography.
Energy Technology Data Exchange (ETDEWEB)
Rodgers, P
1998-03-01
There is more to information than a string of ones and zeroes the ability of ''quantum bits'' to be in two states at the same time could revolutionize information technology. In the mid-1930s two influential but seemingly unrelated papers were published. In 1935 Einstein, Podolsky and Rosen proposed the famous EPR paradox that has come to symbolize the mysteries of quantum mechanics. Two years later, Alan Turing introduced the universal Turing machine in an enigmatically titled paper, On computable numbers, and laid the foundations of the computer industry one of the biggest industries in the world today. Although quantum physics is essential to understand the operation of transistors and other solid-state devices in computers, computation itself has remained a resolutely classical process. Indeed it seems only natural that computation and quantum theory should be kept as far apart as possible surely the uncertainty associated with quantum theory is anathema to the reliability expected from computers? Wrong. In 1985 David Deutsch introduced the universal quantum computer and showed that quantum theory can actually allow computers to do more rather than less. The ability of particles to be in a superposition of more than one quantum state naturally introduces a form of parallelism that can, in principle, perform some traditional computing tasks faster than is possible with classical computers. Moreover, quantum computers are capable of other tasks that are not conceivable with their classical counterparts. Similar breakthroughs in cryptography and communication followed. (author)
Quantum Networks for Generating Arbitrary Quantum States
Kaye, Phillip; Mosca, Michele
2004-01-01
Quantum protocols often require the generation of specific quantum states. We describe a quantum algorithm for generating any prescribed quantum state. For an important subclass of states, including pure symmetric states, this algorithm is efficient.
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.
An Introduction to Quantum Field Theory
Peskin, Michael E
1995-01-01
An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the sta
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 entanglement and quantum operation
Institute of Scientific and Technical Information of China (English)
2008-01-01
It is a simple introduction to quantum entanglement and quantum operations.The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations.It includes remote state preparation by using any pure entangled states,nonlocal operation implementation using entangled states,entanglement capacity of two-qubit gates and two-qubit gates construction.
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.)
Delegating private quantum computations12
Broadbent, Anne
2015-09-01
We give a protocol for the delegation of quantum computation on encrypted data. More specifically, we show that in a client-server scenario, where the client holds the encryption key for an encrypted quantum register held by the server, it is possible for the server to perform a universal set of quantum gates on the quantum data. All Clifford group gates are non-interactive, while the remaining non-Clifford group gate that we implement (the p/8 gate) requires the client to prepare and send a single random auxiliary qubit (chosen among four possibilities), and exchange classical communication. This construction improves on previous work, which requires either multiple auxiliary qubits or two-way quantum communication. Using a reduction to an entanglement-based protocol, we show privacy against any adversarial server according to a simulation-based security definition.
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.
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.
Abrams, D.; Williams, C.
1999-01-01
This thesis describes several new quantum algorithms. These include a polynomial time algorithm that uses a quantum fast Fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases for which all know classical algorithms require exponential time.
Manning, Phillip
2011-01-01
The study of quantum theory allowed twentieth-century scientists to examine the world in a new way, one that was filled with uncertainties and probabilities. Further study also led to the development of lasers, the atomic bomb, and the computer. This exciting new book clearly explains quantum theory and its everyday uses in our world.
Sastry, R R
1999-01-01
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the cosmological constant problem is addressed. The response of an electron to a weak gravitational field (linear approximation) is studied and the order $\\alpha$ correction to the magnetic gravitational moment is computed.
Hadjiivanov, Ludmil
2015-01-01
Expository paper providing a historical survey of the gradual transformation of the "philosophical discussions" between Bohr, Einstein and Schr\\"odinger on foundational issues in quantum mechanics into a quantitative prediction of a new quantum effect, its experimental verification and its proposed (and loudly advertised) applications. The basic idea of the 1935 paper of Einstein-Podolsky-Rosen (EPR) was reformulated by David Bohm for a finite dimensional spin system. This allowed John Bell to derive his inequalities that separate the prediction of quantum entanglement from its possible classical interpretation. We reproduce here their later (1971) version, reviewing on the way the generalization (and mathematical derivation) of Heisenberg's uncertainty relations (due to Weyl and Schr\\"odinger) needed for the passage from EPR to Bell. We also provide an improved derivation of the quantum theoretic violation of Bell's inequalities. Soon after the experimental confirmation of the quantum entanglement (culminati...
Richter, Johannes; Farnell, Damian; Bishop, Raymod
2004-01-01
The investigation of magnetic systems where quantum effects play a dominant role has become a very active branch of solid-state-physics research in its own right. The first three chapters of the "Quantum Magnetism" survey conceptual problems and provide insights into the classes of systems considered, namely one-dimensional, two-dimensional and molecular magnets. The following chapters introduce the methods used in the field of quantum magnetism, including spin wave analysis, exact diagonalization, quantum field theory, coupled cluster methods and the Bethe ansatz. The book closes with a chapter on quantum phase transitions and a contribution that puts the wealth of phenomena into the context of experimental solid-state physics. Closing a gap in the literature, this volume is intended both as an introductory text at postgraduate level and as a modern, comprehensive reference for researchers in the field.
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...
Quantum Mechanics and determinism
Hooft, G. 't
2001-01-01
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied to free Maxwell fields. Lorentz invariance is demonstrated.
Quantum Computation Toward Quantum Gravity
Zizzi, P. A.
2001-08-01
The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin -1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.
A linearization of quantum channels
Crowder, Tanner
2015-06-01
Because the quantum channels form a compact, convex set, we can express any quantum channel as a convex combination of extremal channels. We give a Euclidean representation for the channels whose inverses are also valid channels; these are a subset of the extreme points. They form a compact, connected Lie group, and we calculate its Lie algebra. Lastly, we calculate a maximal torus for the group and provide a constructive approach to decomposing any invertible channel into a product of elementary channels.
Arnold, Michael; Langenbruch, Tobias; Kroha, Johann
2007-11-02
We propose a physical realization of the two-channel Kondo (2CK) effect, where a dynamical defect in a metal has a unique ground state and twofold degenerate excited states. In a wide range of parameters the interactions with the electrons renormalize the excited doublet downward below the bare defect ground state, thus stabilizing the 2CK fixed point. In addition to the Kondo temperature T(K) the three-state defect exhibits another low-energy scale, associated with ground-to-excited-state transitions, which can be exponentially smaller than T(K). Using the perturbative nonequilibrium renormalization group we demonstrate that this can provide the long-sought explanation of the sharp conductance spikes observed by Ralph and Buhrman in ultrasmall metallic point contacts.
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...
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 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.
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
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.
Institute of Scientific and Technical Information of China (English)
ZHOU Nan-run; GONG Li-hua; LIU Ye
2006-01-01
In this letter a cascade quantum teleportation scheme is proposed. The proposed scheme needs less local quantum operations than those of quantum multi-teleportation. A quantum teleportation scheme based on entanglement swapping is presented and compared with the cascade quantum teleportation scheme. Those two schemes can effectively teleport quantum information and extend the distance of quantum communication.
Gudder, Stanley P
2014-01-01
Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism.Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles.The first two chapters survey the ne
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
Garrison, J C
2008-01-01
Quantum optics, i.e. the interaction of individual photons with matter, began with the discoveries of Planck and Einstein, but in recent years it has expanded beyond pure physics to become an important driving force for technological innovation. This book serves the broader readership growing out of this development by starting with an elementary description of the underlying physics and then building up a more advanced treatment. The reader is led from the quantum theory of thesimple harmonic oscillator to the application of entangled states to quantum information processing. An equally impor
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,
Scaling of the local quantum uncertainty at quantum phase transitions
Energy Technology Data Exchange (ETDEWEB)
Coulamy, I.B.; Warnes, J.H.; Sarandy, M.S., E-mail: msarandy@if.uff.br; Saguia, A.
2016-04-29
We investigate the local quantum uncertainty (LQU) between a block of L qubits and one single qubit in a composite system of n qubits driven through a quantum phase transition (QPT). A first-order QPT is analytically considered through a Hamiltonian implementation of the quantum search. In the case of second-order QPTs, we consider the transverse-field Ising chain via a numerical analysis through density matrix renormalization group. For both cases, we compute the LQU for finite-sizes as a function of L and of the coupling parameter, analyzing its pronounced behavior at the QPT. - Highlights: • LQU is suitable for the analysis of block correlations. • LQU exhibits pronounced behavior at quantum phase transitions. • LQU exponentially saturates in the quantum search. • Concavity of LQU indicates criticality in the Ising chain.
Quantum cosmology of (loop) quantum gravity condensates: An example
Gielen, Steffen
2014-01-01
Spatially homogeneous universes can be described in (loop) quantum gravity as condensates of elementary excitations of space. Their treatment is easiest in the second-quantised group field theory formalism which allows the adaptation of techniques from the description of Bose-Einstein condensates in condensed matter physics. Dynamical equations for the states can be derived directly from the underlying quantum gravity dynamics. The analogue of the Gross-Pitaevskii equation defines an anisotropic quantum cosmology model, in which the condensate wavefunction becomes a quantum cosmology wavefunction on minisuperspace. To illustrate this general formalism, we give a mapping of the gauge-invariant geometric data for a tetrahedron to a minisuperspace of homogeneous anisotropic 3-metrics. We then study an example for which we give the resulting quantum cosmology model in the general anisotropic case and derive the general analytical solution for isotropic universes. We discuss the interpretation of these solutions a...
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.
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...
CALL FOR PAPERS: Quantum control
Mancini, Stefano; Wiseman, Howard M.; Man'ko, Vladimir I.
2004-10-01
Over the last few decades, the achievements of highly precise technologies for manipulating systems at quantum scales have paved the way for the development of quantum control. Moreover, the proliferation of results in quantum information suggest that control theory might profitably be re-examined from this perspective. Journal of Optics B: Quantum and Semiclassical Optics will publish a topical issue devoted to quantum control. The Guest Editors invite contributions from researchers working in any area related to quantum control. Topics to be covered include: • Quantum Hamiltonian dynamics and programming control • Quantum decoherence control • Open loop control • Closed loop (feedback) control • Quantum measurement theory • Quantum noise and filtering • Estimation and decision theory • Quantum error correction • Group representation in quantum control • Coherent control in quantum optics and lasers • Coherent control in cavity QED and atom optics • Coherent control in molecular dynamics The topical issue is scheduled for publication in November 2005 and the DEADLINE for submission of contributions is 28 February 2005. All contributions will be peer-reviewed in accordance with the normal refereeing procedures and standards of Journal of Optics B: Quantum and Semiclassical Optics. Submissions should preferably be in either standard LaTeX form or Microsoft Word. Advice on publishing your work in the journal may be found at www.iop.org/journals/authors/jopb. Enquiries regarding this topical issue may be addressed to the Publisher, Dr Claire Bedrock (claire.bedrock@iop.org). There are no page charges for publication. The corresponding author of each paper published will receive a complimentary copy of the topical issue. Contributions to the topical issue should preferably be submitted electronically at www.iop.org/journals/authors/jopb or by e-mail to jopb@iop.org. Authors unable to submit online or by e-mail may send hard copy contributions
Observables in Loop Quantum Gravity with a cosmological constant
Dupuis, Maïté
2013-01-01
An open issue in loop quantum gravity (LQG) is the introduction of a non-vanishing cosmological constant $\\Lambda$. In 3d, Chern-Simons theory provides some guiding lines: $\\Lambda$ appears in the quantum deformation of the gauge group. The Turaev-Viro model, which is an example of spin foam model is also defined in terms of a quantum group. By extension, it is believed that in 4d, a quantum group structure could encode the presence of $\\Lambda\
Buhrman, H; Watrous, J; De Wolf, R; Buhrman, Harry; Cleve, Richard; Watrous, John; Wolf, Ronald de
2001-01-01
Classical fingerprinting associates with each string a shorter string (its fingerprint), such that, with high probability, any two distinct strings can be distinguished by comparing their fingerprints alone. The fingerprints can be exponentially smaller than the original strings if the parties preparing the fingerprints share a random key, but not if they only have access to uncorrelated random sources. In this paper we show that fingerprints consisting of quantum information can be made exponentially smaller than the original strings without any correlations or entanglement between the parties: we give a scheme where the quantum fingerprints are exponentially shorter than the original strings and we give a test that distinguishes any two unknown quantum fingerprints with high probability. Our scheme implies an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity. We optimize several aspects of our scheme.
Curran, Stephen
2009-01-01
In arXiv:0807.0677, K\\"ostler and Speicher observed that de Finetti's theorem on exchangeable sequences has a free analogue if one replaces exchangeability by the stronger condition of invariance under quantum permutations. In this paper we study sequences of noncommutative random variables whose joint distribution is invariant under quantum orthogonal transformations. We prove a free analogue of Freedman's characterization of conditionally independent Gaussian families, namely an infinite sequence of self-adjoint random variables is quantum orthogonally invariant if and only if they form an operator-valued free centered equivariant semicircular family. Similarly, we show that an infinite sequence of noncommutative random variables is quantum unitarily invariant if and only if they form an operator-valued free centered equivariant circular family. We provide an example to show that, as in the classical case, these results fail for finite sequences. We then give an approximation to how far the distribution of ...
Mershin, A; Skoulakis, E M C
2000-01-01
In order to create a novel model of memory and brain function, we focus our approach on the sub-molecular (electron), molecular (tubulin) and macromolecular (microtubule) components of the neural cytoskeleton. Due to their size and geometry, these systems may be approached using the principles of quantum physics. We identify quantum-physics derived mechanisms conceivably underlying the integrated yet differentiated aspects of memory encoding/recall as well as the molecular basis of the engram. We treat the tubulin molecule as the fundamental computation unit (qubit) in a quantum-computational network that consists of microtubules (MTs), networks of MTs and ultimately entire neurons and neural networks. We derive experimentally testable predictions of our quantum brain hypothesis and perform experiments on these.
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".
Haroche, Serge
2013-01-01
Mr Administrator,Dear colleagues,Ladies and gentlemen, “I think I can safely say that nobody understands quantum mechanics”. This statement, made by physicist Richard Feynman, expresses a paradoxical truth about the scientific theory that revolutionised our understanding of Nature and made an extraordinary contribution to our means of acting on and gaining information about the world. In this lecture, I will discuss quantum physics with you by attempting to resolve this paradox. And if I don’...
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....
Diego Martin-Cano, Paloma A. Huidobro, Esteban Moreno; Diego Martin-Cano; Huidobro, Paloma A.; Esteban Moreno; Garcia-Vidal, F.J.
2014-01-01
Quantum plasmonics is a rapidly growing field of research that involves the study of the quantum properties of light and its interaction with matter at the nanoscale. Here, surface plasmons - electromagnetic excitations coupled to electron charge density waves on metal-dielectric interfaces or localized on metallic nanostructures - enable the confinement of light to scales far below that of conventional optics. In this article we review recent progress in the experimental and theoretical inve...
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....
Quantum correlations and distinguishability of quantum states
Spehner, Dominique
2014-07-01
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.
Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map.
Sahlmann, Hanno; Thiemann, Thomas
2012-03-16
We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Lie algebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups.
Zeros and poles of quantum current operators and the condition of quantum integrability
Ding, J; Ding, Jintai; Miwa, Tetsuji
1996-01-01
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we study the zeros and poles of the quantum current operators and present a condition of integrability on the quantum current of $U_q\\left(\\hat{\\frak sl}(2)\\right)$, which is a deformation of the corresponding condition for $\\hat{\\frak sl}(2)$.
Fuchs, Christopher A
2009-01-01
This pseudo-paper consists of excerpts drawn from two of my quantum-email samizdats. Section 1 draws a picture of a physical world whose essence is ``Darwinism all the way down.'' Section 2 outlines how quantum theory should be viewed in light of this, i.e., as being an expression of probabilism (in Bruno de Finetti or Richard Jeffrey's sense) all the way back up. Section 3 describes how the idea of ``identical'' quantum measurement outcomes, though sounding atomistic in character, nonetheless meshes well with a Jamesian style ``radical pluralism.'' Sections 4 and 5 further detail how quantum theory should not be viewed so much as a ``theory of the world,'' but rather as a theory of decision-making for agents immersed within a world of a particular character--the quantum world. Finally, Sections 6 and 7 attempt to sketch the very positive sense in which quantum theory is incomplete, but still just as complete is it can be. In total, I hope these heady speculations convey some of the excitement and potential I...
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.
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
Quantum Central Processing Unit and Quantum Algorithm
Institute of Scientific and Technical Information of China (English)
王安民
2002-01-01
Based on a scalable and universal quantum network, quantum central processing unit, proposed in our previous paper [Chin. Phys. Left. 18 (2001)166], the whole quantum network for the known quantum algorithms,including quantum Fourier transformation, Shor's algorithm and Grover's algorithm, is obtained in a unitied way.
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
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 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)
Mandl, F.
1992-07-01
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 Scientists R. J. Barlow and A. R. Barnett Quantum Mechanics aims to teach those parts of the subject which every physicist should know. The object is to display the inherent structure of quantum mechanics, concentrating on general principles and on methods of wide applicability without taking them to their full generality. This book will equip students to follow quantum-mechanical arguments in books and scientific papers, and to cope with simple cases. To bring the subject to life, the theory is applied to the all-important field of atomic physics. No prior knowledge of quantum mechanics is assumed. However, it would help most readers to have met some elementary wave mechanics before. Primarily written for students, it should also be of interest to experimental research workers who require a good grasp of quantum mechanics without the full formalism needed by the professional theorist. Quantum Mechanics features: A flow diagram allowing topics to be studied in different orders or omitted altogether. Optional "starred" and highlighted sections containing more advanced and specialized material for the more ambitious reader. Sets of problems at the end of each chapter to help student understanding. Hints and solutions to the problems are given at the end of the book.
Loop quantum cosmology: Recent progress
Indian Academy of Sciences (India)
Martin Bojowald
2004-10-01
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is sensitive to the quantum regime. As a consequence, the structure of and the approach to classical singularities are very different from general relativity. The quantum theory is free of singularities, and there are new phenomenological scenarios for the evolution of the very early universe such as inflation. We give an overview of the main effects, focussing on recent results obtained by different groups.
Surface defects and elliptic quantum groups
Yagi, Junya
2017-06-01
A brane construction of an integrable lattice model is proposed. The model is composed of Belavin's R-matrix, Felder's dynamical R-matrix, the Bazhanov-Sergeev-Derkachov-Spiridonov R-operator and some intertwining operators. This construction implies that a family of surface defects act on supersymmetric indices of four-dimensional \\mathcal{N} = 1supersymmetricfieldtheoriesastransfermatricesrelatedtoellipticquantumgroups.
On Integrable Quantum Group Invariant Antiferromagnets
Cuerno, R; Gómez, C
1992-01-01
A new open spin chain hamiltonian is introduced. It is both integrable (Sklyanin`s type $K$ matrices are used to achieve this) and invariant under ${\\cal U}_{\\epsilon}(sl(2))$ transformations in nilpotent irreps for $\\epsilon^3=1$. Some considerations on the centralizer of nilpotent representations and its representation theory are also presented.
Free Quantum Field Theory from Quantum Cellular Automata
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Indian Academy of Sciences (India)
Bipul Saurabh
2017-02-01
For the quantum symplectic group $SP_q(2n)$, we describe the $C^\\ast$-algebra of continuous functions on the quotient space $SP_q(2n)/SP_q(2n − 2)$ as an universal $C^\\ast$-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 representations of the symplectic group due to Zhelobenko. We then exhibit a set of generators of the $K$-groups of this $C^\\ast$-algebra in terms of generators of the $C^\\ast$-algebra.
Hydrophobin-Encapsulated Quantum Dots.
Taniguchi, Shohei; Sandiford, Lydia; Cooper, Maggie; Rosca, Elena V; Ahmad Khanbeigi, Raha; Fairclough, Simon M; Thanou, Maya; Dailey, Lea Ann; Wohlleben, Wendel; von Vacano, Bernhard; de Rosales, Rafael T M; Dobson, Peter J; Owen, Dylan M; Green, Mark
2016-02-01
The phase transfer of quantum dots to water is an important aspect of preparing nanomaterials that are suitable for biological applications, and although numerous reports describe ligand exchange, very few describe efficient ligand encapsulation techniques. In this report, we not only report a new method of phase transferring quantum dots (QDs) using an amphiphilic protein (hydrophobin) but also describe the advantages of using a biological molecule with available functional groups and their use in imaging cancer cells in vivo and other imaging applications.
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...
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...
Fitzpatrick, Richard
2015-01-01
Quantum mechanics was developed during the first few decades of the twentieth century via a series of inspired guesses made by various physicists, including Planck, Einstein, Bohr, Schroedinger, Heisenberg, Pauli, and Dirac. All these scientists were trying to construct a self-consistent theory of microscopic dynamics that was compatible with experimental observations. The purpose of this book is to present quantum mechanics in a clear, concise, and systematic fashion, starting from the fundamental postulates, and developing the theory in as logical manner as possible. Topics covered in the book include the fundamental postulates of quantum mechanics, angular momentum, time-dependent and time-dependent perturbation theory, scattering theory, identical particles, and relativistic electron theory.
Yoshida, Z
2016-01-01
Quantum systems often exhibit fundamental incapability to entertain vortex. The Meissner effect, a complete expulsion of the magnetic field (the electromagnetic vorticity), for instance, is taken to be the defining attribute of the superconducting state. Superfluidity is another, close-parallel example; fluid vorticity can reside only on topological defects with a limited (quantized) amount. Recent developments in the Bose-Einstein condensates produced by particle traps further emphasize this characteristic. We show that the challenge of imparting vorticity to a quantum fluid can be met through a nonlinear mechanism operating in a hot fluid corresponding to a thermally modified Pauli-Schroedinger spinor field. In a simple field-free model, we show that the thermal effect, represented by a nonlinear, non-Hermitian Hamiltonian, in conjunction with spin vorticity, leads to new interesting quantum states; a spiral solution is explicitly worked out.
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.
Feng, Chao-Jun; Li, Xin-Zhou
In this paper, we will give a short review on quantum spring, which is a Casimir effect from the helix boundary condition that proposed in our earlier works. The Casimir force parallel to the axis of the helix behaves very much like the force on a spring that obeys the Hooke's law when the ratio r of the pitch to the circumference of the helix is small, but in this case, the force comes from a quantum effect, so we would like to call it quantum spring. On the other hand, the force perpendicular to the axis decreases monotonously with the increasing of the ratio r. Both forces are attractive and their behaviors are the same in two and three dimensions.
Ranchin, André
2016-01-01
We introduce a new board game based on the ancient Chinese game of Go (Weiqi, Igo, Baduk). The key difference from the original game is that players no longer alternatively play single stones on the board but instead they take turns placing pairs of entangled go stones. A phenomenon of quantum-like collapse occurs when a stone is placed in an intersection directly adjacent to one or more other stones. For each neighboring stone in an entangled pair, each player then chooses which stone of the pair is kept on the board and which stone is removed. The aim of the game is still to surround more territory than the opponent and as the number of stones increases, all the entangled pairs of stones eventually reduce to single stones. Quantum Go provides an interesting and tangible illustration of quantum concepts such as superposition, entanglement and collapse.
Barbara, Bernard; Sawatzky, G; Stamp, P. C. E
2008-01-01
This book is based on some of the lectures during the Pacific Institute of Theoretical Physics (PITP) summer school on "Quantum Magnetism", held during June 2006 in Les Houches, in the French Alps. The school was funded jointly by NATO, the CNRS, and PITP, and entirely organized by PITP. Magnetism is a somewhat peculiar research field. It clearly has a quantum-mechanical basis – the microsopic exchange interactions arise entirely from the exclusion principle, in conjunction with respulsive interactions between electrons. And yet until recently the vast majority of magnetism researchers and users of magnetic phenomena around the world paid no attention to these quantum-mechanical roots. Thus, eg., the huge ($400 billion per annum) industry which manufactures hard discs, and other components in the information technology sector, depends entirely on room-temperature properties of magnets - yet at the macroscopic or mesoscopic scales of interest to this industry, room-temperature magnets behave entirely classic...
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.
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.
The one-way quantum computer - a non-network model of quantum computation
Raussendorf, R; Briegel, H J; Raussendorf, Robert; Browne, Daniel E.; Briegel, Hans J.
2001-01-01
A one-way quantum computer works by only performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the one-way quantum computer. On the other hand, the network model of quantum computation cannot explain all ways of processing quantum information possible with the one-way quantum computer. In this paper, two examples of the non-network character of the one-way quantum computer are given. First, circuits in the Clifford group can be performed in a single time step. Second, the realisation of a particular circuit --the bit-reversal gate-- on the one-way quantum computer has no network interpretation. (Submitted to J. Mod. Opt, Gdansk ESF QIT conference issue.)
Christiansen, Nicolai; Meibohm, Jan; Pawlowski, Jan M; Reichert, Manuel
2015-01-01
We investigate the ultraviolet behaviour of quantum gravity within a functional renormalisation group approach. The present setup includes the full ghost and graviton propagators and, for the first time, the dynamical graviton three-point function. The latter gives access to the coupling of dynamical gravitons and makes the system minimally self-consistent. The resulting phase diagram confirms the asymptotic safety scenario in quantum gravity with a non-trivial UV fixed point. A well-defined Wilsonian block spinning requires locality of the flow in momentum space. This property is discussed in the context of functional renormalisation group flows. We show that momentum locality of graviton correlation functions is non-trivially linked to diffeomorphism invariance, and is realised in the present setup.
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
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
de Bianchi, Massimiliano Sassoli
2013-01-01
In a letter to Born, Einstein wrote: "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...
Bojowald, Martin
1999-01-01
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...
Baaquie, Belal E.
2007-09-01
Foreword; Preface; Acknowledgements; 1. Synopsis; Part I. Fundamental Concepts of Finance: 2. Introduction to finance; 3. Derivative securities; Part II. Systems with Finite Number of Degrees of Freedom: 4. Hamiltonians and stock options; 5. Path integrals and stock options; 6. Stochastic interest rates' Hamiltonians and path integrals; Part III. Quantum Field Theory of Interest Rates Models: 7. Quantum field theory of forward interest rates; 8. Empirical forward interest rates and field theory models; 9. Field theory of Treasury Bonds' derivatives and hedging; 10. Field theory Hamiltonian of forward interest rates; 11. Conclusions; Appendix A: mathematical background; Brief glossary of financial terms; Brief glossary of physics terms; List of main symbols; References; Index.
Bernstein, Jeremy
1991-01-01
For the prominent science writer Jeremy Bernstein, the profile is the most congenial way of communicating science. Here, in what he labels a "series of conversations carried on in the reader's behalf and my own," he evokes the tremendous intellectual excitement of the world of modern physics, especially the quantum revolution. Drawing on his well-known talent for explaining the most complex scientific ideas for the layperson, Bernstein gives us a lively sense of what the issues of quantum mechanics are and of various ways in which individual physicists approached them.The author begins this se
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.
Blind Quantum Signature with Blind Quantum Computation
Li, Wei; Shi, Ronghua; Guo, Ying
2016-12-01
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.
Inhomogenous quantum codes (Ⅰ):additive case
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper,the quantum error-correcting codes are generalized to the inhomogenous quantumstate space Cq1 Cq2 ··· Cqn,where qi(1 i n) are arbitrary positive integers.By attaching an abelian group Ai of order qi to the space Cqi(1 i n),we present the stabilizer construction of such inhomogenous quantum codes,called additive quantum codes,in term of the character theory of the abelian group A = A1⊕A2⊕···⊕An.As usual case,such construction opens a way to get inhomogenous quantum codes from the classical mixed linear codes.We also present Singleton bound for inhomogenous additive quantum codes and show several quantum codes to meet such bound by using classical mixed algebraic-geometric codes.
Discrete quantum geometries and their effective dimension
Thürigen, Johannes
2015-01-01
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the ef...
On The Harmonic Oscillator Group
Lopez, Raquel M; Vega-Guzman, Jose M
2011-01-01
We discuss the maximum kinematical invariance group of the quantum harmonic oscillator from a view point of the Ermakov-type system. The invariance group of generalized driven harmonic oscillator is shown to be isomorphic to the corresponding Schroedinger group of the free particle.
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.
Ashmead, John
2010-01-01
Normally we quantize along the space dimensions but treat time classically. But from relativity we expect a high level of symmetry between time and space. What happens if we quantize time using the same rules we use to quantize space? To do this, we generalize the paths in the Feynman path integral to include paths that vary in time as well as in space. We use Morlet wavelet decomposition to ensure convergence and normalization of the path integrals. We derive the Schr\\"odinger equation in four dimensions from the short time limit of the path integral expression. We verify that we recover standard quantum theory in the non-relativistic, semi-classical, and long time limits. Quantum time is an experiment factory: most foundational experiments in quantum mechanics can be modified in a way that makes them tests of quantum time. We look at single and double slits in time, scattering by time-varying electric and magnetic fields, and the Aharonov-Bohm effect in time.
1993-05-14
Barbara , California, March 1993. I Carrier Dynamics in Quantum Wires Investigators: Wolfgang Porod I I Using the Monte Carlo technique, we have...8217.ubtle correlations between impunty scanenng events tin the "res;ence oft a ma.’neuc fle!dlp which are beyond Fermi’s Golden Rule. In this caper . we
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 treate
Lanzagorta, Marco O.; Gomez, Richard B.; Uhlmann, Jeffrey K.
2003-08-01
In recent years, computer graphics has emerged as a critical component of the scientific and engineering process, and it is recognized as an important computer science research area. Computer graphics are extensively used for a variety of aerospace and defense training systems and by Hollywood's special effects companies. All these applications require the computer graphics systems to produce high quality renderings of extremely large data sets in short periods of time. Much research has been done in "classical computing" toward the development of efficient methods and techniques to reduce the rendering time required for large datasets. Quantum Computing's unique algorithmic features offer the possibility of speeding up some of the known rendering algorithms currently used in computer graphics. In this paper we discuss possible implementations of quantum rendering algorithms. In particular, we concentrate on the implementation of Grover's quantum search algorithm for Z-buffering, ray-tracing, radiosity, and scene management techniques. We also compare the theoretical performance between the classical and quantum versions of the algorithms.
Energy Technology Data Exchange (ETDEWEB)
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.
Cheon, Taksu; Tsutsui, Izumi; Fülöp, Tamás
2004-09-01
We show that the point interactions on a line can be utilized to provide U(2) family of qubit operations for quantum information processing. Qubits are realized as states localized in either side of the point interaction which represents a controllable gate. The qubit manipulation proceeds in a manner analogous to the operation of an abacus.
Keimer, Bernhard; Sachdev, Subir
2011-01-01
This is a review of the basic theoretical ideas of quantum criticality, and of their connection to numerous experiments on correlated electron compounds. A shortened, modified, and edited version appeared in Physics Today. This arxiv version has additional citations to the literature.
Peschanski, R
1993-01-01
Phenomenological and theoretical aspects of fragmentation for elementary particles (resp. nuclei) are discussed. It is shown that some concepts of classical fragmentation remain relevant in a microscopic framework, exhibiting non-trivial properties of quantum relativistic field theory (resp. lattice percolation). Email contact: pesch@amoco.saclay.cea.fr
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.
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...
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
On the tomographic picture of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ibort, A., E-mail: albertoi@math.uc3m.e [Departamento de Matematicas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganes, Madrid (Spain); Man' ko, V.I., E-mail: manko@na.infn.i [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, G., E-mail: marmo@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Simoni, A., E-mail: simoni@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Ventriglia, F., E-mail: ventriglia@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy)
2010-06-07
We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by means of Naimark positive definite functions on the Weyl-Heisenberg group. This connection is used to formulate properties which guarantee that tomographic probabilities describe quantum states in the probability representation of quantum mechanics.
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
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
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, secu
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.
2016-05-01
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.
Quantum Secure Dialogue with Quantum Encryption
Ye, Tian-Yu
2014-09-01
How to solve the information leakage problem has become the research focus of quantum dialogue. In this paper, in order to overcome the information leakage problem in quantum dialogue, a novel approach for sharing the initial quantum state privately between communicators, i.e., quantum encryption sharing, is proposed by utilizing the idea of quantum encryption. The proposed protocol uses EPR pairs as the private quantum key to encrypt and decrypt the traveling photons, which can be repeatedly used after rotation. Due to quantum encryption sharing, the public announcement on the state of the initial quantum state is omitted, thus the information leakage problem is overcome. The information-theoretical efficiency of the proposed protocol is nearly 100%, much higher than previous information leakage resistant quantum dialogue protocols. Moreover, the proposed protocol only needs single-photon measurements and nearly uses single photons as quantum resource so that it is convenient to implement in practice.
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.
Introduction to quantum spin systems
Directory of Open Access Journals (Sweden)
A. Langari
2008-06-01
Full Text Available This manuscript is the collection of lectures given in the summer school on strongly correlated electron systems held at Isfahan university of technology, June 2007. A short overview on quantum magnetism and spin systems is presented. The numerical exact diagonalization (Lanczos alghorithm is explained in a pedagogical ground. This is a method to get some ground state properties on finite cluster of lattice models. Two extensions of Lanczos method to get the excited states and also finite temperature properties of quantum models are also explained. The basic notions of quantum phase transition is discussed in term of Ising model in transverse field. Its phase diagram and critical properties are explained using the quantum renormalization group approach. Most of the topics are in tutorial level with hints to recent research activities.
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.
Efficient quantum walk on a quantum processor
Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiao-Qi; O'Brien, Jeremy; Wang, Jingbo; Matthews, Jonathan
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 frame- work for developing new quantum algorithms. In this paper, 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 ef...
Interpreting Quantum Discord in Quantum Metrology
Girolami, Davide
2015-01-01
Multipartite quantum systems show properties which do not admit a classical explanation. In particular, even nonentangled states can enjoy a kind of quantum correlations called quantum discord. I discuss some recent results on the role of quantum discord in metrology. Given an interferometric phase estimation protocol where the Hamiltonian is initially unknown to the experimentalist, the quantum discord of the probe state quantifies the minimum precision of the estimation. This provides a phy...
Quantum Mechanics interpreted in Quantum Real Numbers
Corbett, J V; Corbett, John V; Durt, Thomas
2002-01-01
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms of quantum mechanics are re-interpreted. Our aim is to show that, when formulated in the language of quantum real numbers, the laws of quantum mechanics appear more natural, less counterintuitive than when they are presented in terms of standard numbers.
Quantum transitions and quantum entanglement from Dirac-like dynamics simulated by trapped ions
Bittencourt, Victor A. S. V.; Bernardini, Alex E.; Blasone, Massimo
2016-05-01
Quantum transition probabilities and quantum entanglement for two-qubit states of a four-level trapped ion quantum system are computed for time-evolving ionic states driven by Jaynes-Cummings Hamiltonians with interactions mapped onto a SU(2 )⊗SU(2 ) group structure. Using the correspondence of the method of simulating a 3 +1 dimensional Dirac-like Hamiltonian for bispinor particles into a single trapped ion, one preliminarily obtains the analytical tools for describing ionic state transition probabilities as a typical quantum oscillation feature. For Dirac-like structures driven by generalized Poincaré classes of coupling potentials, one also identifies the SU(2 )⊗SU(2 ) internal degrees of freedom corresponding to intrinsic parity and spin polarization as an adaptive platform for computing the quantum entanglement between the internal quantum subsystems which define two-qubit ionic states. The obtained quantum correlational content is then translated into the quantum entanglement of two-qubit ionic states with quantum numbers related to the total angular momentum and to its projection onto the direction of the trapping magnetic field. Experimentally, the controllable parameters simulated by ion traps can be mapped into a Dirac-like system in the presence of an electrostatic field which, in this case, is associated to ionic carrier interactions. Besides exhibiting a complete analytical profile for ionic quantum transitions and quantum entanglement, our results indicate that carrier interactions actively drive an overall suppression of the quantum entanglement.
Spin network quantum simulator
Energy Technology Data Exchange (ETDEWEB)
Marzuoli, Annalisa; Rasetti, Mario
2002-12-30
We propose a general setting for a universal representation of the quantum structure on which quantum information stands, whose dynamical evolution (information manipulation) is based on angular momentum recoupling theory. Such scheme complies with the notion of 'quantum simulator' in the sense of Feynman, and is shown to be related with the topological quantum field theoretical approach to quantum computation.
Hoehn, Philipp A
2016-01-01
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 `catalogue of knowledge' about S; no ontic assumptions are necessary. From the rules we derive the state spaces for N qubits and show that (a) they coincide with the set of density matrices over N qubit Hilbert spaces; (b) states evolve unitarily under the group $\\rm{PSU}(2^N)$ according to the von Neumann evolution equation; and (c) the binary questions by means of which O interrogates the systems corresponds to projective measurements on Pauli operators with outcome probabilities given by the Born rule. Besides offering a novel conceptual perspective on qubit quantum theory, the reconstruction also unravels new structural insights. Namely, we show that, in a quadratic information measure, (d) qubits satisfy informational complementarity inequalities...
Shaw, Bilal A
2010-01-01
Steganography is the process of hiding secret information by embedding it in an "innocent" message. We present protocols for hiding quantum information in a codeword of a quantum error-correcting code passing through a channel. Using either a shared classical secret key or shared entanglement the sender (Alice) disguises her information as errors in the channel. The receiver (Bob) can retrieve the hidden information, but an eavesdropper (Eve) with the power to monitor the channel, but without the secret key, cannot distinguish the message from channel noise. We analyze how difficult it is for Eve to detect the presence of secret messages, and estimate rates of steganographic communication and secret key consumption for certain protocols.
Energy Technology Data Exchange (ETDEWEB)
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.
Häring, Reto Andreas
1993-01-01
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same representation category. In this paper we try to establish that every quantum field theory satisfying some basic axioms posseses a weak quasi Hopf algebra as gauge symmetry. The first step is to construct a functor from the representation category to the category of finite dimensional vector spaces. Given such a functor we can use a generalized reconstruction theorem to find the symmetry algebra. It is shown how this symmetry algebra is used to build a gauge covariant field algebra and we investigate the question why this generality is necessary.
Mould, Richard A
1999-01-01
In a previous paper, the author proposed a quantum mechanical interaction that would insure that the evolution of subjective states would parallel the evolution of biological states, as required by von Neumann's theory of measurement. The particular model for this interaction suggested an experiment that the author has now performed wih negative results. A modified model is outlined in this paper that preserves the desirable features of the original model, and is consistent with the experimen...
Ecker, Gerhard
2005-01-01
After a brief historical review of the emergence of QCD as the quantum field theory of strong interactions, the basic notions of colour and gauge invariance are introduced leading to the QCD Lagrangian. The second lecture is devoted to perturbative QCD, from tree-level processes to higher-order corrections in renormalized perturbation theory, including jet production in e+ e- annihilation, hadronic tau decays and deep inelastic scattering. The final two lectures treat various aspects of QCD b...
Information transfer through quantum channels
Energy Technology Data Exchange (ETDEWEB)
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
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-12-01
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.
Invariant measures on multimode quantum Gaussian states
Lupo, C; De Pasquale, A; Facchi, P; Florio, G; Pascazio, S
2012-01-01
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 or applications in quantum optics and quantum information.
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.
The flat phase of quantum polymerized membranes
Coquand, O
2016-01-01
We investigate the flat phase of quantum polymerized phantom membranes by means of a nonperturbative renormalization group approach. We first implement this formalism for general quantum polymerized membranes and derive the flow equations that encompass both quantum and thermal fluctuations. We then deduce and analyze the flow equations relevant to study the flat phase and discuss their salient features : quantum to classical crossover and, in each of these regimes, strong to weak coupling crossover. We finally illustrate these features in the context of free standing graphene physics.
Coordinate time dependence in Quantum Gravity
Bojowald, M; Skirzewski, A; Bojowald, Martin; Singh, Parampreet; Skirzewski, Aureliano
2004-01-01
The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. Using ingredients of the group averaging method to solve constraints one can nevertheless introduce a classical coordinate time into the quantum theory, and use it to investigate the way a semiclassical continuous description emerges from discrete quantum evolution. Applying this technique to test effective classical equations of loop cosmology and their implications for inflation and bounces, we show that the effective semiclassical theory is in good agreement with the quantum description even at short scales.
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.
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.
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.
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.
Hui, Ning-Ju; Xu, Yang-Yang; Wang, Jicheng; Zhang, Yixin; Hu, Zheng-Da
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.
Coherent Dynamics of Complex Quantum Systems
Akulin, Vladimir M
2006-01-01
A large number of modern problems in physics, chemistry, and quantum electronics require a consideration of population dynamics in complex multilevel quantum systems. The purpose of this book is to provide a systematic treatment of these questions and to present a number of exactly solvable problems. It considers the different dynamical problems frequently encountered in different areas of physics from the same perspective, based mainly on the fundamental ideas of group theory and on the idea of ensemble average. Also treated are concepts of complete quantum control and correction of decoherence induced errors that are complementary to the idea of ensemble average. "Coherent Dynamics of Complex Quantum Systems" is aimed at senior-level undergraduate students in the areas of Atomic, Molecular, and Laser Physics, Physical Chemistry, Quantum Optics and Quantum Informatics. It should help them put particular problems in these fields into a broader scientific context and thereby take advantage of the well-elabora...
Mixing properties of stochastic quantum Hamiltonians
Onorati, E; Kliesch, M; Brown, W; Werner, A H; Eisert, J
2016-01-01
Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and quantum information theory. In this work, we present a framework describing the mixing properties of continuous-time unitary evolutions originating from local Hamiltonians having time-fluctuating terms, reflecting a Brownian motion on the unitary group. The induced stochastic time evolution is shown to converge to a unitary design. As a first main result, we present bounds to the mixing time. By developing tools in representation theory, we analytically derive an expression for a local k-th moment operator that is entirely independent of k, giving rise to approximate unitary k-designs and quantum tensor product expanders. As a second main result, we introduce tools for proving bounds on the rate of decoupling from an environment with random quantum processes. By tying the mathema...
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
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.
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.
Quantum probability and quantum decision-making.
Yukalov, V I; Sornette, D
2016-01-13
A rigorous general definition of quantum probability is given, which is valid not only for elementary events but also for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision-making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.
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 mechanics and the psyche
Galli Carminati, G.; Martin, F.
2008-07-01
In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.