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 Phenomenological quantum thermodynamics resource theory for closed bipartite Schottky systems

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190173 ◽  
Author(s):  
Wolfgang Muschik
Keyword(s):  
Quantum Mechanics ◽  
Density Operator ◽  
Nonequilibrium Thermodynamics ◽  
Discrete Systems ◽  
Resource Theory ◽  
Quantum Thermodynamics ◽  
Theme Issue ◽  
Von Neumann ◽  
Starting Point ◽  
Von Neumann Equation

How to introduce thermodynamics to quantum mechanics? From numerous possibilities of solving this task, the simple choice is here: the conventional von Neumann equation deals with a density operator whose probability weights are time-independent. Because there is no reason apart from the reversible quantum mechanics that these weights have to be time-independent, this constraint is waived, which allows one to introduce thermodynamical concepts to quantum mechanics. This procedure is similar to that of Lindblad’s equation, but different in principle. But beyond this simple starting point, the applied thermodynamical concepts of discrete systems may perform a ‘source theory’ for other versions of phenomenological quantum thermodynamics. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

scholarly journals Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Jeong Ryeol Choi
Keyword(s):  
Hamiltonian Dynamics ◽  
Adiabatic Invariant ◽  
Time Dependent ◽  
Adiabatic Invariants ◽  
Superconducting Qubit ◽  
Computing Systems ◽  
Nanomechanical Resonator ◽  
Von Neumann ◽  
Superconducting Circuit ◽  
Von Neumann Equation

An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.

scholarly journals Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1219
Author(s):  
Zeyi Shi ◽  
Sumiyoshi Abe
Keyword(s):  
Time Evolution ◽  
Open Quantum System ◽  
Dynamical Evolution ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Completely Positive Map ◽  
Expectation Values ◽  
Completely Positive ◽  
Temporal Asymmetry ◽  
Von Neumann

Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital, in contrast to the fact that monotonic increases of both the von Neumann entropy and Rényi entropy require the map to be unital. In this way, the weak invariants describe temporal asymmetry in a manner different from the entropies. A formula is presented for time evolution of the covariance matrix associated with the weak invariants in cases where the system density matrix obeys the Gorini–Kossakowski–Lindblad–Sudarshan equation.

Further Development of a Model for Predicting Corrosion Fatigue Crack Growth in Reactor Pressure Vessel Steels

1987 ◽  
Vol 109 (3) ◽  
pp. 340-346 ◽  
Author(s):  
J. D. Gilman
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Alloy Steel ◽  
High Stress ◽  
Time Dependent ◽  
Crack Advance ◽  
Low Alloy Steel ◽  
Time Rate ◽  
Paris Law

Analysis of fatigue crack growth data for low-alloy steel shows that the influence of cyclic frequency in simulated LWR environments can be interpreted as the superposition of a time-dependent, corrosion-assisted crack growth rate upon an increment predicted by a Paris law. The time-dependent component increases monotonically to a maximum of about 6×10−5 mm/s as stress cycling becomes more aggressive. A useful measure of aggressiveness is the average time rate of crack advance due to the Paris law component alone; i.e., AΔKn × frequency. The result suggests that current ASME Code methods for flaw assessment are highly conservative in some regimes of stress and frequency, but there is a possibility of growth rates well above the ASME XI, Appendix A curves in a very low-frequency, high-stress regime. An upper bound to the time rate of corrosion-assisted crack growth in low-alloy steel is well supported by the data. The threshold conditions for the onset of this high rate are less well defined and require further investigation.

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.

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