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Information Theory and Semi-Quantum Maxent

Angel Ricardo Plastino, Claudia M. Sarris

Published Mar 21, 2014• 0 citations
OpenAlex

Abstract

This books presents a detailed treatment of the physics of the interaction between quantum and classical variables. Semiquantum Hamiltonians represent mixed physical systems for which one part is quantal and the other classical. These parts are coupled in nonlinear fashion. The coupling term contains both quantum and classical degrees of freedom. Physical systems that are appropriately described in this way are are to be found in molecular and solid state physics. Of course, so described is the interaction between a classical measurement's instrument and the quantum system being measured. Semiquantum systems have a technological counterpart as well, in connection with nano-technology (molecular transistors, quantum dots and SQUIDS, for instance). These special systems can be successfully modelled by quantum billiards, dynamic system in which a particle alternates between motion in a straight line and elastic reflections from a boundary. The interest focuses in vibrating quantum billiards, in which a particle of mass m is subjected to elastic interactions confined in a potential well V(q), generated by a classical mass M.

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This book attempts to convey to the reader that semiclassical physics can be fun, as well as useful for understanding quantum fluctuations in interacting many-body systems. It presents applications to finite fermion systems in diverse areas of physics.

CRC Press eBooks•Mar 5, 2018•648 citations
This books presents a detailed treatment of the physics of the interaction between quantum and classical variables. Semiquantum Hamiltonians represent mixed physical systems for which one part is quantal and the other classical. These parts are coupled in nonlinear fashion. The coupling term contains both quantum and classical degrees of freedom. Physical systems that are appropriately described in this way are are to be found in molecular and solid state physics. Of course, so described is the interaction between a classical measurement's instrument and the quantum system being measured. Semiquantum systems have a technological counterpart as well, in connection with nano-technology (molecular transistors, quantum dots and SQUIDS, for instance). These special systems can be successfully modelled by quantum billiards, dynamic system in which a particle alternates between motion in a straight line and elastic reflections from a boundary. The interest focuses in vibrating quantum billiards, in which a particle of mass m is subjected to elastic interactions confined in a potential well V(q), generated by a classical mass M.
We examine the quantum motion of two particles interacting through a contact force which are confined in a rectangular domain in two and three dimensions. When there is a difference in the mass scale of two particles, adiabatic separation of the fast and slow variables can be performed. Appearance of the Berry phase and magnetic flux is pointed out. The system is reduced to a one-particle Aharonov-Bohm billiard in two-dimensional case. In three dimension, the problem effectively becomes the motion of a particle in the presence of closed flux string in a box billiard. 3.65.Bz, 5.45.+b, 11.27.+d Typeset using REVTEX 1 The quantum billiard problem has been instrumental in revealing non-trivial features of seemingly simple systems with minimal degrees of freedom. As a consequence, unlike real-world billiards, quantum physicists ’ version of the billiard problem has only one particle moving within a walled boundary. The dynamics is controlled by the shape of the boundary,
Quantum information is an emerging field which has attracted a lot of attention in the last couple of decades. It is a broad subject which extends from the most applied questions (e.g. how to build quantum computers or secure cryptographic systems) to the most theoretical problems concerning the formalism and interpretation of quantum mechanics, its complexity, and its potential to go beyond classical physics. This book is an introduction to quantum information with special emphasis on continuous-variable systems (such as light) which can be described as collections of harmonic oscillators. It covers a selection of basic concepts, focusing on their physical meaning and mathematical treatment. It starts from the very first principles of quantum mechanics, and builds up the concepts and techniques following a logical progression. This is an excellent reference for students with a full semester of standard quantum mechanics and researchers in closely related fields.
Quantum information is an emerging field which has attracted a lot of attention in the last couple of decades. It is a broad subject which extends from the most applied questions (e.g. how to build quantum computers or secure cryptographic systems) to the most theoretical problems concerning the formalism and interpretation of quantum mechanics, its complexity, and its potential to go beyond classical physics. This book is an introduction to quantum information with special emphasis on continuous-variable systems (such as light) which can be described as collections of harmonic oscillators. It covers a selection of basic concepts, focusing on their physical meaning and mathematical treatment. It starts from the very first principles of quantum mechanics, and builds up the concepts and techniques following a logical progression. This is an excellent reference for students with a full semester of standard quantum mechanics and researchers in closely related fields.
Superconducting circuits, photonic cavities, and tiny mechanical oscillators are versatile systems in which quantum dynamics can be observed and controlled. These various technologies can be combined, and the resulting “circuits” are often referred to as nano-electromechanical or optomechanical systems. In the context of quantum physics, such devices are referred to as “mesoscopic” because they contain a large number of atoms. This terminology distinguishes them from the “microscopic” systems of atom-optics, such as single ions [364] and atoms [545, 233, 26], and the spins of individual nuclei [412]. Nano-engineered systems provide an especially powerful arena for exploring quantum measurement and control because of their potential to realize complex circuits. In this chapter we explain how to treat these systems and describe in detail a common method used to measure them. Superconducting circuits The electrical circuits that we describe in this chapter are quite different from those that use normal conductors, such as copper wire at room temperature. Normal conductors are subject to strong dissipation and decoherence from the environment. As a result the dynamical degrees of freedom of the circuits, the currents and voltages, behave as classical variables. In superconducting circuits, the resistance, and thus the dissipation, is so small that the currents and voltages behave as quantum mechanical degrees of freedom. Of course, the current in a wire is actually composed of many elementary particles that each obey quantum mechanics. Why then should the current act like a single quantum degree of freedom? A mechanical analogy is useful here. Recall that even though a macroscopic pendulum is composed of many particles, when one talks about the motion of the pendulum one means the motion of the center-of-mass of its constituent particles. Since the center of mass is merely a linear combination of the coordinates of each particle, it is itself a valid quantum mechanical coordinate with a conjugate momentum. In a similar way the total current in a superconducting wire is a collective degree of freedom that obeys quantum mechanics.
Abstract According to the Berry–Tabor conjecture, the spectral properties of typical nonrelativistic quantum systems with an integrable classical counterpart agree with those of Poissonian random numbers. We investigate to what extend it applies to relativistic neutrino billiards (NBs) consisting of a spin-1/2 particle confined to a bounded planar domain by imposing suitable boundary conditions (BCs). In distinction to nonrelativistic quantum billiards (QBs), NBs do not have a well-defined classical counterpart. However, the peaks in the length spectra, that is, the modulus of the Fourier transform of the spectral density from wave number to length, of NBs are just like for QBs at the lengths of periodic orbits of the classical billiard (CB). This implies that there must be a connection between NBs and the dynamic of the CB. We demonstrate that NBs with shapes of circle- and ellipse-sectors with an integrable classical dynamic, obtained by cutting the circle and ellipse NB along symmetry lines, have no common eigenstates with the latter and that, indeed, their spectral properties can be similar to those of classically chaotic QBs. These features orginate from the intermingling of symmetries of the spinor components and the discontinuity in the BCs leading to contradictory conditional equations at corners connecting curved and straight boundary parts. To corroborate the necessity of the curved boundary part in order to generate GOE-like behavior, we furthermore consider the right-angled triangle NB constructed by halving the equilateral-triangle NB along a symmetry axis. For an understanding of these findings in terms of purely classical quantities we use the semiclassical approach recently developed for massive NBs, and Poincaré–Husimi distributions of the eigenstates in classical phase space. The results indicate, that in the ultrarelativistic limit these NBs do not show the behavior expected for classically chaotic QBs.