It is shown that the order property of pure bipartite states under stochastic local operations and classical communications (SLOCC) changes radically when dimensionality shifts from finite to infinite. In contrast to finite-dimensional systems where there is no pure incomparable state, the existence of infinitely many mutually SLOCC incomparable states is shown for infinite-dimensional systems even under the bounded energy and finite information exchange condition. These results show that the effect of the infinite dimensionality of Hilbert space, the ``infinite workspace'' property, remains even in physically relevant infinite-dimensional systems.It is shown that the order property of pure bipartite states under stochastic local operations and classical communications (SLOCC) changes radically when dimensionality shifts from finite to infinite. In contrast to finite-dimensional systems where there is no pure incomparable state, the existence of infinitely many mutually SLOCC incomparable states is shown for infinite-dimensional systems even under the bounded energy and finite information exchange condition. These results show that the effect of the infinite dimensionality of Hilbert space, the ``infinite workspace'' property, remains even in physically relevant infinite-dimensional systems.

arXiv:quant-ph/0406141Physical Review ANov 23, 200413 citations

Closed Systems

P. Singha Deo

Springer eBooksJan 1, 20210 citations

Introduction

D.Ya. Petrina, V.I. Gerasimenko, P V Malyshev

In the present monograph, we study infinite classical statistical systems, i.e., systems of infinitely many particles in the infinite phase space. The states of these systems are completely defined by infinite sequences of correlation functions. The key problem of statistical mechanics is to determine the state of a many-particle system at any time if the initial state is known, i.e., to determine its evolution. The other important problem is to determine and investigate equilibrium (stationary) states of statistical systems.In the present monograph, we study infinite classical statistical systems, i.e., systems of infinitely many particles in the infinite phase space. The states of these systems are completely defined by infinite sequences of correlation functions. The key problem of statistical mechanics is to determine the state of a many-particle system at any time if the initial state is known, i.e., to determine its evolution. The other important problem is to determine and investigate equilibrium (stationary) states of statistical systems.

CRC Press eBooksApr 11, 20020 citations

Closed Systems

P. Singha Deo, Kanchan Meena

Springer eBooksJan 1, 20240 citations

Random Nonlinear Infinite-Level-System Model for Amorphous Solid Phonon Echo and Saturation Phenomena

Zhou, Di, Anthony J. Leggett

The first two successful predictions for amorphous solid experiments by tunneling-two-level-system (TTLS) was phonon echo and saturation phenomena. In this paper by generalizing TTLS to infinite-level-system model with certain randomness and nonlinearity, we prove that phonon echo is a stimulated emission process. The classical infinite-level-system (taking $\hbar\to 0$ limit) cannot find saturation effect, while quantum infinite-level-system can find it with certain nonlinearity assumed. We also prove that without randomness or nonlinearity neither phonon echo nor saturation exists in arbitrary infinite-level-system.The first two successful predictions for amorphous solid experiments by tunneling-two-level-system (TTLS) was phonon echo and saturation phenomena. In this paper by generalizing TTLS to infinite-level-system model with certain randomness and nonlinearity, we prove that phonon echo is a stimulated emission process. The classical infinite-level-system (taking $\hbar\to 0$ limit) cannot find saturation effect, while quantum infinite-level-system can find it with certain nonlinearity assumed. We also prove that without randomness or nonlinearity neither phonon echo nor saturation exists in arbitrary infinite-level-system.

arXiv:1510.05538Oct 19, 20152 citations

Some Simple Systems

K. Tamvakis

Undergraduate texts in physicsJan 1, 20190 citations

\hbar\to 0

limit) cannot find saturation effect, while quantum infinite-level-system can find it with certain nonlinearity assumed. We also prove that without randomness or nonlinearity neither phonon echo nor saturation exists in arbitrary infinite-level-system.