Convergence of the von-neumann equation towards the quantum bolt/maim equation in a deterministic framework

1999 ◽  
Vol 329 (3) ◽  
pp. 231-236 ◽  
Author(s):  
François Castella ◽  
Pierre Degond
Keyword(s):  
Von Neumann ◽  
Von Neumann Equation ◽  
Deterministic Framework

scholarly journals ENTANGLEMENT DYNAMICS IN FINITE QUDIT CHAIN IN CONSISTENT MAGNETIC FIELD

2012 ◽  
Vol 10 (06) ◽  
pp. 1250068 ◽  
Author(s):  
E. A. IVANCHENKO
Keyword(s):  
Magnetic Field ◽  
Entanglement Dynamics ◽  
Von Neumann ◽  
Magnetic Field Modulation ◽  
Entanglement Measures ◽  
Analytical Formulae ◽  
Initial States ◽  
Von Neumann Equation ◽  
Field Modulation ◽  
The Magnetic Field

Based on the Liouville–von Neumann equation, we obtain a closed system of equations for the description of a qutrit or coupled qutrits in an arbitrary, time-dependent, external magnetic field. The dependence of the dynamics on the initial states and the magnetic field modulation is studied analytically and numerically. We compare the relative entanglement measure's dynamics in bi-qudits with permutation particle symmetry. We find the magnetic field modulation which retains the entanglement in the system of two coupled qutrits. Analytical formulae for the entanglement measures in finite chains from two to six qutrits or three quartits are presented.

scholarly journals Concepts of Phenomenological Irreversible Quantum Thermodynamics I: Closed Undecomposed Schottky Systems in Semi-Classical Description

2019 ◽  
Vol 44 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Wolfgang Muschik
Keyword(s):  
Time Dependent ◽  
Quantum Thermodynamics ◽  
Time Rate ◽  
Von Neumann ◽  
Classical Description ◽  
Von Neumann Equation

Abstract If the von Neumann equation is modified by time dependent statistical weights, the time rate of entropy, the entropy exchange and the production of a Schottky system are derived whose Hamiltonian does not contain the interaction with the system’s environment. This interaction is semi-classically described by the quantum theoretical expressions of power and entropy exchange.

scholarly journals PARAMETRIC DOWN CONVERSION OF A BOSONIC THERMOFIELD VACUUM

2012 ◽  
Vol 27 (22) ◽  
pp. 1250124 ◽  
Author(s):  
THIAGO PRUDÊNCIO
Keyword(s):  
Input State ◽  
Von Neumann ◽  
Vacuum States ◽  
Parametric Down Conversion ◽  
Von Neumann Equation ◽  
Down Conversion

We consider a process of parametric down conversion where the input state is a bosonic thermofield vacuum. This state leads to a parametric down conversion, generating an output of two excited photons. Following a thermofield dynamics scheme, the input state, initially in a bosonic thermofield vacuum, and the output states, initially in vacuum states, evolve under a Liouville–von Neumann equation.

On the derivation of the Pauli and van Hove master equations

1978 ◽  
Vol 56 (9) ◽  
pp. 1204-1217 ◽  
Author(s):  
K. M. van Vliet
Keyword(s):  
Projection Operator ◽  
Evolution Operator ◽  
Random Phase ◽  
Stochastic Theory ◽  
Operator Method ◽  
Original Method ◽  
Von Neumann ◽  
Projection Operator Method ◽  
Von Neumann Equation ◽  
Pauli Master Equation

We discuss the derivation of the Pauli master equation, based on a repeated random phase assumption, and of van Hove's result, based on an initial random phase assumption. For the former we indicate a derivation which is closer to the general approach of stochastic theory than Pauli's original method. For the van Hove result, we show that the diagonal and nondiagonal parts of the evolution operator of the Schrödinger or von Neumann equation are readily obtained by Zwanzig's projection operator method.

Modulational instability analysis of the cylindrical nonlinear von Neumann equation

2013 ◽  
Vol 79 (4) ◽  
pp. 443-446 ◽  
Author(s):  
R. FEDELE ◽  
A. MANNAN ◽  
F. TANJIA ◽  
S. DE NICOLA ◽  
D. JOVANOVIĆ ◽  
...  
Keyword(s):  
Theoretical Investigation ◽  
Modulational Instability ◽  
Dispersion Relations ◽  
Instability Analysis ◽  
Von Neumann ◽  
Functional Forms ◽  
Von Neumann Equation ◽  
Statistical Approaches

AbstractA theoretical investigation of both deterministic and statistical approaches to modulational instability arising in the cylindrical nonlinear von Neumann equation (CNLvNE) is carried out. This is done on the basis of a recently discovered exact mapping that relates the CNLvNE to the standard one. We show that the dispersion relations of the cylindrical case (for the examples considered here) do not depend explicitly on time and their functional forms do not change with respect to the corresponding standard cases. These results differ from the previous investigations.

Verallgemeinerte physikalische Entropien auf informationstheoretischer Grundlage

1965 ◽  
Vol 20 (12) ◽  
pp. 1543-1553 ◽  
Author(s):  
H. Schwegler
Keyword(s):  
Density Operator ◽  
Gibbs Equation ◽  
Macroscopic Equation ◽  
Von Neumann ◽  
Special Cases ◽  
Self Consistent ◽  
Von Neumann Equation ◽  
The Times ◽  
Experimental Values ◽  
Special Case

Physical entropies SB are defined with respect to a certain set of variables, the observationlevel B. For all times in which B exists, SB is the uncertainty H of a density operator RB making H a maximum with respect to the experimental values of B. This definition is not restricted to the thermodynamic equilibrium. The entropies SB measure the vagueness of the description in Hilbert-space caused by the choice of B. The time dependence of the density operator RB is not governed by the von Neumann equation, but in the special case of a “self-consistent“ B it may be calculated with the help of this equation. An increasing SB is obtained.If the times for which B exists are sufficiently close, a macroscopic equation for the time deriva· tive of SB is given. Three special cases of B are considered, leading to the Gibbs equation, a generalized entropy equation for heat conduction and an entropy equation for the multipole relaxation.

scholarly journals Exact decoherence brought by one internal degree of freedom: von Neumann equation approach and examples

2019 ◽  
Vol 33 (24) ◽  
pp. 1950285
Author(s):  
John Paul A. Besagas ◽  
Jan Carlo L. Lima ◽  
Eric A. Galapon
Keyword(s):  
Composite System ◽  
Initial Conditions ◽  
Measurement Model ◽  
Factorization Method ◽  
Internal Degree ◽  
Degree Of Freedom ◽  
Von Neumann ◽  
Von Neumann Equation ◽  
Internal Degree Of Freedom ◽  
Joint State

In a quantum measurement setting, it is known that environment-induced decoherence theory describes the emergence of effectively classical features of the quantum system–measuring apparatus composite system when the apparatus is allowed to interact with the environment. In [E. A. Galapon, Europhys. Lett. 113, 60007 (2016)], a measurement model is found to have the feature of inducing exact decoherence at a finite time via one internal degree of freedom of the apparatus provided that the apparatus is decomposed into a pointer and an inaccessible probe, with the pointer and the probe being in momentum-limited initial states. However, an issue can be raised against the model: while the factorization method of the time-evolution operator used there is formally correct, it is not completely rigorous due to some unstated conditions on the validity of the factorization in the Hilbert space of the model. Furthermore, no examples were presented there in implementing the measurement scheme in specific quantum systems. The goal of this paper is to re-examine the model and confirm its features independently by solving the von Neumann equation for the joint state of the composite system as a function of time. This approach reproduces the joint state obtained in the original work, leading to the same conditions for exact decoherence and orthogonal pointer states when the required initial conditions on the probe and pointer are imposed. We illustrate the exact decoherence process in the measurement of observables of a spin-1/2 particle and a quantum harmonic oscillator by using the model.

Short-time Chebyshev propagator for the Liouville–von Neumann equation

1999 ◽  
Vol 110 (14) ◽  
pp. 6626-6634 ◽  
Author(s):  
Hua Guo ◽  
Rongqing Chen
Keyword(s):  
Von Neumann ◽  
Von Neumann Equation ◽  
Short Time
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