scholarly journals NONLINEAR EXTENSIONS OF SCHRÖDINGER–VON NEUMANN QUANTUM DYNAMICS: A SET OF NECESSARY CONDITIONS FOR COMPATIBILITY WITH THERMODYNAMICS

2005 ◽  
Vol 20 (13) ◽  
pp. 977-984 ◽  
Author(s):  
GIAN PAOLO BERETTA
Keyword(s):  
Quantum Dynamics ◽  
Necessary Conditions ◽  
Experimental Tests ◽  
Microscopic Level ◽  
General Description ◽  
Von Neumann ◽  
Nonequilibrium States ◽  
Nonlinear Extensions ◽  
Isolated Systems ◽  
True Quantum

We propose a list of conditions that consistency with thermodynamics imposes on linear and nonlinear generalizations of standard unitary quantum mechanics that assume a set of true quantum states without the restriction ρ2 = ρ even for strictly isolated systems and that are to be considered in experimental tests of the existence of intrinsic (spontaneous) decoherence at the microscopic level. As part of the discussion, we present a general description of nonequilibrium states.

Dynamics of Interacting Classical and Quantum Systems

2011 ◽  
Vol 18 (04) ◽  
pp. 339-351 ◽  
Author(s):  
Dariusz Chruściński ◽  
Andrzej Kossakowski ◽  
Giuseppe Marmo ◽  
E. C. G. Sudarshan
Keyword(s):  
Characteristic Feature ◽  
Quantum Dynamics ◽  
Quantum Discord ◽  
Main Idea ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Quantum States ◽  
Algebra Of Observables ◽  
Classical Quantum ◽  
True Quantum

We analyze the dynamics of coupled classical and quantum systems. The main idea is to treat both systems as true quantum ones and impose a family of superselection rules which imply that the corresponding algebra of observables of one subsystem is commutative and hence may be treated as a classical one. Equivalently, one may impose a special symmetry which restricts the algebra of observables to the 'classical' subalgebra. The characteristic feature of classical-quantum dynamics is that it leaves invariant a subspace of classical-quantum states, that is, it does not create quantum correlations as measured by the quantum discord.

On the Global Quantum Dynamics of Multi- Lattice Systems with Non-linear Classical Effects

1988 ◽  
Vol 43 (6) ◽  
pp. 521-532 ◽  
Author(s):  
E. Duffner ◽  
A. Rieckers
Keyword(s):  
Quantum Dynamics ◽  
Quantum Systems ◽  
Lattice Systems ◽  
Von Neumann ◽  
Weakly Continuous ◽  
Lattice Quantum ◽  
Pure Phase ◽  
Non Linear ◽  
Algebraic Concepts ◽  
Linear Differential

Abstract The microscopic dynamics for a class of long range interacting multi-lattice quantum systems is constructed in the thermodynamical limit by means of operator algebraic concepts. By direct estimations the existence of the limiting Schrödinger dynamics is proven for a set of states, which comprises also globally non-equilibrium situations. The expectation values of the classical observables in the pure phase states are shown to satisfy a set of coupled non-linear differential equations. The limiting Heisenberg dynamics is derived as a W*-automorphism group in the partially universal von Neumann algebra which corresponds to the selected set of states; it is in general, however, not σ-weakly continuous in the time parameter.

Boltzmann Entropy & Equilibrium in Non-Isolated Systems

2017 ◽  
pp. 74-92 ◽  
Author(s):  
Alberto Gianinetti
Keyword(s):  
Statistical Mechanics ◽  
Stable Condition ◽  
Microscopic Level ◽  
Boltzmann Entropy ◽  
Microscopic Approach ◽  
Macroscopic Level ◽  
Probable Distribution ◽  
Isolated Systems ◽  
Most Probable Distribution

The microscopic approach of statistical mechanics has developed a series of formal expressions that, depending on the different features of the system and/or process involved, allow for calculating the value of entropy from the microscopic state of the system. This value is maximal when the particles attain the most probable distribution through space and the most equilibrated sharing of energy between them. At the macroscopic level, this means that the system is at equilibrium, a stable condition wherein no net statistical force emerges from the overall behaviour of the particles. If no force is available then no work can be done and the system is inert. This provides the bridge between the probabilistic equilibration that occurs at the microscopic level and the classical observation that, at a macroscopic level, a system is at equilibrium when no work can be done by it.

Generalized measurements

2009 ◽  
Author(s):  
Stephen Barnett
Keyword(s):  
Quantum Theory ◽  
Theory Of Measurement ◽  
Mathematical Formulation ◽  
Hermitian Operator ◽  
Physical Nature ◽  
Measurement Process ◽  
General Description ◽  
Von Neumann ◽  
Measured System ◽  
The Relationship

Extracting information from a quantum system inevitably requires the performance of a measurement, and it is no surprise that the theory of measurement plays a central role in our subject. The physical nature of the measurement process remains one of the great philosophical problems in the formulation of quantum theory. Fortunately, however, it is sufficient for us to take a pragmatic view by asking what measurements are possible and how the theory describes them, without addressing the physical mechanism of the measurement process. This is the approach we shall adopt. We shall find that it leads us to a powerful and general description of both the probabilities associated with measurement outcomes and the manner in which the observation transforms the quantum state of the measured system. The simplest form of measurement was given a mathematical formulation by von Neumann, and we shall refer to measurements of this type as von Neumann measurements or projective measurements. It is this description of measurements that is usually introduced in elementary quantum theory courses. We start with an observable quantity A represented by a Hermitian operator Â, the eigenvalues of which are the possible results of the measurement of A. The relationship between the operator, its eigenstates {|λnñ}, and its (real) eigenvalues {λn} is expressed by the eigenvalue equation . . . Â |λn_ = λn|λn_. (4.1) . . .

A model of quantum-von Neumann hybrid cellular automata: principles and simulation of quantum coherent superposition and dehoerence in cytoskeletal microtubules

2015 ◽  
Vol 15 (1&2) ◽  
pp. 22-36
Author(s):  
Manuel Alfonseca ◽  
Alfonso Ortega ◽  
Marina de la Cruz ◽  
Stuart R. Hameroff ◽  
Rafael Lahoz-Beltra
Keyword(s):  
Wave Function ◽  
Cellular Automata ◽  
Biological Function ◽  
Stable State ◽  
Microscopic Level ◽  
Quantum Biology ◽  
Wave Function Collapse ◽  
Von Neumann ◽  
Hybrid Cellular Automata ◽  
Coherent Superposition

Although experimental evidence suggests the influence of quantum effects in living organisms, one of the most critical problems in quantum biology is the explanation of how those effects that take place in a microscopic level can manifest in the macroscopic world of living beings. At present, quantum decoherence associated with the wave function collapse is one of the most accepted mechanisms explaining how the classical world of living beings emerges from the quantum world. Whatever the cause of wave function collapse, there exist biological systems where a biological function arises as a result of this collapse (e.g. birds navigation, plants photosynthesis, sense of smell, etc.), as well as the opposite examples (e.g. release of energy from ATP molecules at actomyosin muscle) where a biological function takes place in a quantum coherent environment. In this paper we report the modelling and simulation of quantum coherent superposition in cytoskeletal microtubules including decoherence, thus the effect of the collapse of the microtubule coherent state wave function. Our model is based on a new class of hybrid cellular automata (QvN), capable of performing as either a quantum cellular automata (QCA) or as a classical von Neumann automata (CA). These automata are able to simulate the transition or reduction from a quantum microscopic level with superposition of several quantum states, to a macroscopic level with a single stable state. Our results illustrate the significance of quantum biology explaining the emergence of some biological functions. We believe that in the future quantum biology will have a deep effect on the design of new devices, e.g. quantum hardware, in electrical engineering.

scholarly journals PATTERN FORMATION IN QUANTUM ENSEMBLES

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1570-1592
Author(s):  
ANTONINA N. FEDOROVA ◽  
MICHAEL G. ZEITLIN
Keyword(s):  
Pattern Formation ◽  
Complex Systems ◽  
Quantum Dynamics ◽  
Bbgky Hierarchy ◽  
Stable States ◽  
Localized Modes ◽  
Collective Models ◽  
Von Neumann ◽  
Methods Analytical ◽  
Quantum Ensembles

We present a family of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from basic localized modes in various collective models arising from the quantum hierarchy of Wigner-von Neumann-Moyal-Lindblad equations, which are the result of "wignerization" procedure of classical BBGKY hierarchy. We present the explicit description of internal quantum dynamics by means of exact analytical/numerical computations.

scholarly journals Testing the Orientability of Time

2018 ◽  
Author(s):  
Mark Hadley
Keyword(s):  
Quantum Theory ◽  
Time Reversal ◽  
Experimental Tests ◽  
Theoretical Work ◽  
Microscopic Level ◽  
Local Realism ◽  
Quantum Theories ◽  
Time Direction ◽  
Recent Theoretical Work ◽  
Interpretation Of Quantum Theory

A number of experimental tests of time orientability are described as well as clear experimental signatures from non time orientability (time reversal). Some tests are well known, while others are based on more recent theoretical work. Surprisingly, the results all suggest that time is not orientable at a microscopic level; even definitive tests are positive. At a microscopic level the direction of time can reverse and a consistent forward time direction cannot be defined. That is the conclusion supported by a range of well-known experiments. The conflict between quantum theory and local realism; electrodynamics with electric charges; and spin half transformation properties of fermions; can all be interpreted as evidence of time reversal. While particle-antiparticle annihilation provides a definitive test. It offers both a new view of space-time and an novel interpretation of quantum theory with the potential to unify classical and quantum theories.

scholarly journals Probing leptogenesis

2018 ◽  
Vol 33 (05n06) ◽  
pp. 1842005 ◽  
Author(s):  
E. J. Chun ◽  
G. Cvetič ◽  
P. S. B. Dev ◽  
M. Drewes ◽  
C. S. Fong ◽  
...  
Keyword(s):  
Beta Decay ◽  
Neutrino Oscillation ◽  
Necessary Conditions ◽  
Experimental Tests ◽  
Neutrinoless Double Beta Decay ◽  
Double Beta Decay ◽  
Symmetric Model ◽  
High Scale ◽  
Heavy Leptons ◽  
Neutral Heavy Leptons

The focus of this paper lies on the possible experimental tests of leptogenesis scenarios. We consider both leptogenesis generated from oscillations, as well as leptogenesis from out-of-equilibrium decays. As the Akhmedov–Rubakov–Smirnov (ARS) mechanism allows for heavy neutrinos in the GeV range, this opens up a plethora of possible experimental tests, e.g. at neutrino oscillation experiments, neutrinoless double beta decay, and direct searches for neutral heavy leptons at future facilities. In contrast, testing leptogenesis from out-of-equilibrium decays is a quite difficult task. We comment on the necessary conditions for having successful leptogenesis at the TeV-scale. We further discuss possible realizations and their model specific testability in extended seesaw models, models with extended gauge sectors, and supersymmetric leptogenesis. Not being able to test high-scale leptogenesis directly, we present a way to falsify such scenarios by focusing on their washout processes. This is discussed specifically for the left–right symmetric model and the observation of a heavy [Formula: see text], as well as model independently when measuring [Formula: see text] washout processes at the LHC or neutrinoless double beta decay.

scholarly journals Lagrange problem for fractional ordinary elliptic system via Dubovitskii–Milyutin method

2020 ◽  
Vol 25 (2) ◽  
Author(s):  
Dariusz Idczak ◽  
Stanisław Walczak
Keyword(s):  
Maximum Principle ◽  
Elliptic System ◽  
Fractional Laplacian ◽  
Dirichlet Boundary ◽  
Necessary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Von Neumann ◽  
Weak Maximum Principle ◽  
Operator Calculus ◽  
Lagrange Problem

In the paper, we investigate a weak maximum principle for Lagrange problem described by a fractional ordinary elliptic system with Dirichlet boundary conditions. The Dubovitskii–Milyutin approach is used to find the necessary conditions. The fractional Laplacian is understood in the sense of Stone–von Neumann operator calculus.

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