Dynamical Localization in Disordered Quantum Spin Systems

We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following main results: First, for general systems with short range interactions, dynamical localization implies exponential decay of ground state correlations, up to an explicit correction. Second, the dynamical localization of random xy spin chains can be reduced to dynamical localization of an effective one-particle Hamiltonian. In particular, the isotropic xy chain in random exterior magnetic field is dynamically localized.     

Quantum Dynamical Recurrences in Position-Dependent Mass Systems

Journal of Russian Laser Research - Wave-packet dynamics in bounded systems manifests quantum recurrences at different time scales, namely, classical periodicity, quantum revivals, and fractional...     

Nonlinear Dynamical Symmetries of Some Two-Dimensional Quantum Systems

In this paper nonlinear dynamical symmetries of three quantum systems are studied in detail, such as theKepler-Coulomb system and the isotropic harmonic oscillator in a two-dimensional curved space, and the generalizedpseudo-oscillators in the two-dimensional flat space. Their nonlinear spectrum generating algebras are shown to berelevant to polynomial angular momentum algebras.     

A Note on Quantum Bell Nonlocality and Quantum Entanglement for High Dimensional Quantum Systems

We study the Bell nonlocality of high dimensional quantum systems based on quantum entanglement. A quantitative relationship between the maximal expectation value B of Bell operators and the quantum entanglement concurrence C is obtained for even dimension pure states, with the upper and lower bounds of B governed by C.

     

Generalized Conditional Entropies of Partitions on Quantum Logic

For partitions on quantum logic, the Rényi and Tsallis conditional entropies are introduced. Several relations between the conditional entropies of such partitions are derived.     

Dynamical Suppression of Nonlocal Decoherence in Two-State Quantum Systems

Nonlocal decoherence of two qubits due to Pure phase damping has been investigated. We have proposed a scheme to keep the entanglement of two qubits from nonlocal decoherence. By applying a series of ±π pulses, nonlocal decoherence can be thoroughly suppressed.     

Transformation Properties of Dynamical Systems at the Quantum Level

Based on the generating functional of Green function for a dynamical system, the general equations of transformation properties at the quantum level are derived. In some cases they can be reduced to the quantum Noether theorem. In some other cases they can be reduced to momentum theorem or angular momentum theorem etc. at the quantum level. An example is presented and it shows that the classical conservation laws don’t always preserve in quantum theories. PACS: 11.10.E     

A Note on the Time Development of Quantum Lattice Systems

The time development of quantum lattice systems is studied without any restrictions on the growth condition of the potential . A thermodynamic limit of quantum Gibbs state, a *-algebra and an automorphism group _t for which is a KMS state are constructed.     

量子系统的动力学对称性研究与代数动力学

文章介绍了量子系统的动力学对称性理论和代数动力学在人造了系统和量子光学系统中的应用。     

A Family of Monotone Quantum Relative Entropies

We study here the elementary properties of the relative entropy ${\mathcal{H}_\varphi(A, B) = {\rm Tr}[\varphi(A) - \varphi(B) - \varphi'(B)(A - B)]}$ for φ a convex function and A, B bounded self-adjoint operators. In particular, we prove that this relative entropy is monotone if and only if φ′ is operator monotone. We use this to appropriately define ${\mathcal{H}_\varphi(A, B)}$ in infinite dimension.     

Dynamical Suppression of Pure Amplitude Damping in Two-State Quantum Systems

Dynamical control of decoherence induced by the environment in a single quantum-bit system is investigated. We choose the suitable perturbations acting on the qubit system to decrease the decoherence due to pure amplitude damping. The scheme proposed here is based on the free-Hamiltonian-elimination technique and the paritykick technique, which concludes two homogeneous classical large-blue-detuned optical fields with different frequencies added to the qubit system. By applying this scheme, the decoherence can be completely suppressed.     

A New Dynamical Reflection Algebra and Related Quantum Integrable Systems

We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang?CBaxter equations, coactions, fusions, and commuting traces are derived. Explicit examples are given and quantum integrable Hamiltonians are constructed. They exhibit features similar to the Ruijsenaars?CSchneider Hamiltonians.     

Theory of Dynamical Systems and the Relations Between Classical and Quantum Mechanics

We give a review of some works where it is shown that certain quantum-like features are exhibited by classical systems. Two kinds of problems are considered. The first one concerns the specific heat of crystals (the so called Fermi–Pasta–Ulam problem), where a glassy behavior is observed, and the energy distribution is found to be of Planck-like type. The second kind of problems concerns the self-interaction of a charged particle with the electromagnetic field, where an analog of the tunnel effect is proven to exist, and moreover some nonlocal effects are exhibited, leading to a natural hidden variable theory which violates Bell's inequalities.     

Introductive Backgrounds to Modern Quantum Mathematics with Application to Nonlinear Dynamical Systems

Introductive backgrounds to a new mathematical physics discipline—Quantum Mathematics—are discussed and analyzed both from historical and from analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1932, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered. The Authors devote their article to their Friend and Teacher academician Prof. Anatoliy M. Samoilenko on occasion of his 70 years-Birthday with great compliments and gratitude to his brilliant talent and impressive impact to modern theory of nonlinear dynamical systems of mathematical physics and nonlinear analysis     

Two-Parameter Entropies in Extended Parastatistics of Nonextensive Systems

Russian Physics Journal - General expressions are given for entropies from which one-parameter and two-parameter entropies for quantum nonextensive systems follow in extended parastatistics.     

Growing Classical and Quantum Entropies in the Early Universe

Following the idea that the global and local arrow of time has a cosmological origin, we define an entropy in the classical and in the quantum periods of the universe evolution. For the quantum period a semi-classical approach is adopted, modelling the universe with Wheeler-De Witt equation and using WKB. By applying the self-induced decoherence to the state of the universe it is proved that the quantum universe becomes a classical one. This allows us to define a conditional entropy which, in our simplified model, is proportional to e ^{2γ t} where γ is the dumping factor associated with the interaction potential of the scalar fields. Finally we find both Gibbs and thermodynamical entropy of the universe based in the conditional entropy.     

A Note on Quantum Coherence

In this paper, we discuss the coherence of the reduced state in system H _A ?H _B under taking different quantum operations acting on subsystem H _B . Firstly, we show that for a pure bipartite state, the coherence of the final subsystem H _A under the sum of two orthonormal rank 1 projections acting on H _B is less than or equal to the sum of the coherence of the state after two orthonormal projections acting on H _B , respectively. Secondly, we obtain that the coherence of reduced state in subsystem H _A under random unitary channel \({\Phi }(\rho )={\sum }_{s}\lambda _{s}U_{s}\rho U_{s}^{\ast }\) acting on H _B , is equal to the coherence of the state after each operation \({\Phi }_{s}(\rho )=\lambda _{s}U_{s}\rho U_{s}^{\ast }\) acting on H _B for every s. In addition, for general quantum operation \({\Phi }(\rho )={\sum }_{s}F_{s}\rho F_{s}^{\ast }\) on H _B , we get the relation

$$ C\left (\left ((I\otimes {\Phi })\rho ^{AB}\right )^{A}\right )\leq \sum \limits _{s}C\left (\left ((I\otimes {\Phi }_{s})\rho ^{AB}\right )^{A}\right ). $$

     

Exchange Dynamical Quantum Groups

For any simple Lie algebra ? and any complex number q which is not zero or a nontrivial root of unity, %but may be equal to 1 we construct a dynamical quantum group (Hopf algebroid), whose representation theory is essentially the same as the representation theory of the quantum group U _q (?). This dynamical quantum group is obtained from the fusion and exchange relations between intertwining operators in representation theory of U _q (?), and is an algebraic structure standing behind these relations. Received: 24 March 1998 / Accepted: 14 February 1999