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S. V. Kozyrev

Publications and source records attributed to S. V. Kozyrev.

64 records · Page 4Linked to original sources
arXiv2000

On the structure of Markov flows

A new infinitesimal characterization of completely positive but not necessarily homomorphic Markov flows from a C^*-algebra to bounded operators on the boson Fock space over L^2(R) is given. Contrarily to previous characterizations, based on stochastic differential equations, this characterization is universal, i.e. valid for arbitrary Markov flows. With this result the study of Markov flows is reduced to the study of four C_0-semigroups. This includes the classical case and even in this case it seems to be new. The result is applied to deduce a new existence theorem for Markov flows.

quant-ph↗
arXiv1999

The stochastic limit of quantum spin systems

The stochastic limit for the system of spins interacting with a boson field is investigated. In the finite volume an application of the stochastic golden rule shows that in the limit the dynamics of a quantum system is described by a quantum white noise equation that after taking of normal order is equivalent to quantum stochastic differential equation (QSDE). For the quantum Langevin equation the dynamics is well defined and is a quantum flow on the infinite lattice system.

quant-ph↗
arXiv1999

Non-Exponential Decay for Polaron Model

A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We compute matrix elements of the evolution operator in the stochastic approximation and show that depending on the state of the particle one can get the non-exponential decay with the rate t^{-3/2}. In the process of computation a new algebra of commutational relations that can be considered as an operator deformation of quantum Boltzmann commutation relations is used.

quant-ph↗
arXiv1999

Application of p-adic analysis to models of spontaneous breaking of the replica symmetry

Methods of p-adic analysis are applied to the investigation of the spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for the replica matrix is given and moreover the replica matrix in the models of spontaneous breaking of the replica symmetry in the simplest case is expressed in the form of the Vladimirov operator of p-adic fractional differentiation. Also the model of hierarchical diffusion (that was proposed to describe relaxation of spin glasses) investigated using p-adic analysis.

cond-mat.dis-nn↗
arXiv1998

Dynamical q-deformation in quantum theory and the stochastic limit

A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We show that the field operators obey q-commutation relations with q depending on time. After the stochastic (or van Hove) limit, due to the nonlinearity, the atomic and field degrees of freedom become entangled in the sense that the field and the atomic variables no longer commute but give rise to a new algebra with new commutation relations replacing the Boson ones. This new algebra allows to give a simple proof of the fact that the non crossing half-planar diagrams give the dominating contribution in a weak coupling regime and to calculate explicitly the correlations associated to the new algebra. The above results depend crucially on the fact that we do not introduce any dipole or multipole approximation.

math.QA↗
arXiv1997

Dynamics of Dissipative Two-Level Systems in the Stochastic Approximation

The dynamics of the spin-boson Hamiltonian is considered in the stochastic approximation. The Hamiltonian describes a two-level system coupled to an environment and is widely used in physics, chemistry and the theory of quantum measurement. We demonstrate that the method of the stochastic approximation which is a general method of consideration of dynamics of an arbitrary system interacting with environment is powerful enough to reproduce qualitatively striking results by Leggett at al. found earlier for this model. The result include an exact expression of the dynamics in terms of the spectral density and show an appearance of two most interesting regimes for the system, i.e. pure oscillating and pure damping ones. Correlators describing environment are also computed.

quant-ph↗
arXiv1997

Free coherent states and $p$-adic numbers

Free coherent states for a system with two degrees of freedom is defined. Existence of the homeomorphism of the ring of integer 2-adic numbers to the set of coherent states corresponding to an eigenvalue of the operator of annihilation is proved. It is shown that the metric of free Fock space induces the 2-adic topology on the set of coherent states.

q-alg↗
arXiv1995

The Master Field for Large $N$ Matrix Models and Quantum Groups

In recent works by Singer, Douglas and Gopakumar and Gross an application of results of Voiculescu from non-commutative probability theory to constructions of the master field for large $N$ matrix field theories have been suggested. In this note we consider interrelations between the master field and quantum groups. We define the master field algebra and observe that it is isomorphic to the algebra of functions on the quantum group $SU_q(2)$ for $q=0$. The master field becomes a central element of the quantum group Hopf algebra. The quantum Haar measure on the $SU_q(2)$ for any $q$ gives the Wigner semicircle distribution for the master field. Coherent states on $SU_q(2)$ become coherent states in the master field theory.

hep-th↗
arXiv1994

The Stable Representation of the algebra of functions on the quantum group $SU_{q}(2)$

An operation of a coproduct of representations of a bialgebra is defined. The coproduct operation for representations of the Hopf algebra of functions on the quantum group $SU_{q}(2)$ is investigated. A notion of a stable representation $Π$ is introdused. This means that the representation $Π$ is invariant under coproduct by arbitrary representation. Algebra of functions on the quantum group $SU_{q}(2)$ in the representation $Π$ is a factor of a type II$_{\infty}$. Formula for the trace in the representation $Π$ is given . The invariant integral of Woronovich on $SU_{q}(2)$ will take the form $\int f dμ= tr(f cc^{*})$.

hep-th↗