scholarly journals Classical analogue of the statistical operator

Open Physics ◽  
2014 ◽  
Vol 12 (3) ◽  
Author(s):  
Angelo Plastino ◽  
Angel Plastino ◽  
Claudia Zander
Keyword(s):  
Density Matrix ◽  
Quantum Mechanical ◽  
Marginal Probability ◽  
Marginal Density ◽  
Partial Trace ◽  
Statistical Correlations ◽  
Composite Systems ◽  
Probability Densities ◽  
Classical Analogue ◽  
Statistical Operator

AbstractWe advance the notion of a classical density matrix, as a classical analogue of the quantum mechanical statistical operator, and investigate its main properties. In the case of composite systems a partial trace-like operation performed upon the global classical density matrix leads to a marginal density matrix describing a subsystem. In the case of dynamically independent subsystems (that is, non-interacting subsystems) this marginal density matrix evolves locally, its behavior being completely determined by the local phase-space flow associated with the subsystem under consideration. However, and in contrast with the case of ordinary marginal probability densities, the marginal classical density matrix contains information concerning the statistical correlations between a subsystem and the rest of the system.

A Determinantal Inequality Involving Partial Traces

2016 ◽  
Vol 59 (3) ◽  
pp. 585-591 ◽  
Author(s):  
Minghua Lin
Keyword(s):  
Density Matrix ◽  
Partial Trace ◽  
Determinantal Inequality ◽  
Math Phys

AbstractLet A be a density matrix in . Audenaert [J. Math. Phys. 48(2007) 083507] proved an inequality for Schatten p-norms:where Tr1 and Tr2 stand for the first and second partial trace, respectively. As an analogue of his result, we prove a determinantal inequality

scholarly journals DEFORMED DENSITY MATRIX AND GENERALIZED UNCERTAINTY RELATION IN THERMODYNAMICS

2004 ◽  
Vol 19 (01) ◽  
pp. 71-81 ◽  
Author(s):  
A. E. SHALYT-MARGOLIN ◽  
A. YA. TREGUBOVICH
Keyword(s):  
Statistical Mechanics ◽  
Density Matrix ◽  
Uncertainty Relation ◽  
Planck Scale ◽  
Additional Term ◽  
Temperature Limit ◽  
Quantum Mechanical ◽  
Uncertainty Relations ◽  
Primary Object ◽  
Complete Analogy

A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the lower limit of inverse temperature. In our opinion the approach proposed may lead to the proofs of these relations. To this end, the statistical mechanics deformation at Planck scale. The statistical mechanics deformation is constructed by analogy to the earlier quantum mechanical results. As previously, the primary object is a density matrix, but now the statistical one. The obtained deformed object is referred to as a statistical density pro-matrix. This object is explicitly described, and it is demonstrated that there is a complete analogy in the construction and properties of quantum mechanics and statistical density matrices at Planck scale (i.e. density pro-matrices). It is shown that an ordinary statistical density matrix occurs in the low-temperature limit at temperatures much lower than the Planck's. The associated deformation of a canonical Gibbs distribution is given explicitly.

Probability relations between separated systems

1936 ◽  
Vol 32 (3) ◽  
pp. 446-452 ◽  
Author(s):  
E. Schrödinger
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Pure State ◽  
Relativistic Quantum ◽  
Present Theory ◽  
Relativistic Quantum Mechanics ◽  
Quantum Mechanical ◽  
Alternative Possibility ◽  
Linearly Independent ◽  
Statistical Operator

The paper first scrutinizes thoroughly the variety of compositions which lead to the same quantum-mechanical mixture (as opposed to state or pure state). With respect to a given mixture every state has a definite probability (or mixing fraction) between 0 and 1 (including the limits), which is calculated from the mixtures Statistical Operator and the wave function of the state in question.A well-known example of mixtures occurs when a system consists of two separated parts. If the wave function of the whole system is known, either part is in the situation of a mixture, which is decomposed into definite constituents by a definite measuring programme to be carried out on the other part. All the conceivable decompositions (into linearly independent constituents) of the first system are just realized by all the possible measuring programmes that can be carried out on the second one. In general every state of the first system can be given a finite chance by a suitable choice of the programme.It is suggested that these conclusions, unavoidable within the present theory but repugnant to some physicists including the author, are caused by applying non-relativistic quantum mechanics beyond its legitimate range. An alternative possibility is indicated.

DIFFUSION DEPENDING ON LINEAR MOMENTUM FOR CONTINUUM STATES

2012 ◽  
Vol 26 (04) ◽  
pp. 1250005 ◽  
Author(s):  
WERNER SCHEID ◽  
AURELIAN ISAR ◽  
AUREL SANDULESCU
Keyword(s):  
Density Matrix ◽  
Wave Packets ◽  
Linear Momentum ◽  
Quantum Mechanical ◽  
Continuum States ◽  
Mechanical Diffusion

Based on the Lindblad theory we study a quantum mechanical diffusion which depends only on the operator of the linear momentum and acts on the density matrix of wave packets. The density is assumed initially as coherent and gets incoherently with time.

scholarly journals Probability Densities of Superconductors

2014 ◽  
Vol 41 ◽  
pp. 31-44
Author(s):  
K.A.I.L. Wijewardena Gamalath ◽  
G.D.K.N. Udeni
Keyword(s):  
Probability Density ◽  
Cooper Pair ◽  
Radial Wave Function ◽  
Classical Particle ◽  
Quantum Mechanical ◽  
Ginzburg Landau ◽  
Radial Wave ◽  
Energy Current ◽  
Probability Densities ◽  
Zero Momentum

The energy, current density and momentum probability densities of superconductors were studied from London, Ginzburg-Landau and BSC theories by treating cooper pair as a particle moving in a magnetic field through analytical and numerical techniques. The London and GL solution were exactly the same at the classical limit for NbN. Considering a Cooper pair as a complete classical particle, the momentum probability density was derived by using the Maxwell velocity distribution and the quantum mechanical momentum probability density was derived by using the radial wave function of the cooper pairs for Zn. The quantum mechanical and classical momentum probability densities overlap at zero momentum.

scholarly journals Quantum Harmonic Analysis of the Density Matrix

Quanta ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 74 ◽  
Author(s):  
Maurice A. De Gosson
Keyword(s):  
Density Matrix ◽  
Harmonic Analysis ◽  
Quantum Mechanical ◽  
Mixed States ◽  
Density Matrices ◽  
Planck’S Constant ◽  
Planck's Constant

We will study rigorously the notion of mixed states and their density matrices. We will also discuss the quantum-mechanical consequences of possible variations of Planck's constant h. This review has been written having in mind two readerships: mathematical physicists and quantum physicists. The mathematical rigor is maximal, but the language and notation we use throughout should be familiar to physicists.Quanta 2018; 7: 74–110.

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