Asymmetric Time Evolution and Reduced Dynamics

2011 ◽  
Vol 18 (02) ◽  
pp. 157-163
Author(s):  
Peter W. Bryant
Keyword(s):  
Quantum Theory ◽  
Time Evolution ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Time Coordinate ◽  
Mechanical Environment ◽  
Measurable Difference ◽  
Asymmetric Quantum ◽  
Symmetric Theory

When using a time asymmetric quantum theory, one must identify the time evolution parameter with a duration in time rather than with a time coordinate value. This identification restricts the options for the quantum mechanical environment of open quantum systems. The restriction may be important for interpretational questions concerning irreversibility or entanglement, but there is no measurable difference between a reduced dynamics within a time symmetric theory or within a time asymmetric theory.

scholarly journals On individuality in quantum theory

2015 ◽  
Vol 13 (1) ◽  
pp. 29-38
Author(s):  
Jasmina Jeknic-Dugic
Keyword(s):  
Quantum Theory ◽  
Structural Realism ◽  
Mechanical Analysis ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Ontic Structural Realism

A quantum mechanical analysis of the decomposability of quantum systems into subsystems provides support for the so-called "attenuated Eliminative Ontic Structural Realism" within Categorical Structuralism studies in physics. Quantum subsystems are recognized as non-individual, relationally defined objects that deflate or relax some standard objections against Eliminative Ontic Structural Realism. Our considerations assume the universally valid quantum theory without tackling interpretational issues.

Interpolation of matrices and matrix-valued densities: The unbalanced case

2018 ◽  
Vol 30 (3) ◽  
pp. 458-480 ◽  
Author(s):  
YONGXIN CHEN ◽  
TRYPHON T. GEORGIOU ◽  
ALLEN TANNENBAUM
Keyword(s):  
Open Quantum Systems ◽  
Wasserstein Distance ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Frobenius Norm ◽  
Spatial Dependency ◽  
Lindblad Equation ◽  
Optimal Mass Transport ◽  
Mechanical Formulation ◽  
The Matrix

We propose unbalanced versions of the quantum mechanical version of optimal mass transport that is based on the Lindblad equation describing open quantum systems. One of them is a natural interpolation framework between matrices and matrix-valued measures via a quantum mechanical formulation of Fisher-Rao information and the matricial Wasserstein distance, and the second is an interpolation between Wasserstein distance and Frobenius norm. We also give analogous results for the matrix-valued density measures, i.e., we add a spatial dependency on the density matrices. This might extend the applications of the framework to interpolating matrix-valued densities/images with unequal masses.

scholarly journals Fermionic duality: General symmetry of open systems with strong dissipation and memory

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Valentin Bruch ◽  
Konstantin Nestmann ◽  
Jens Schulenborg ◽  
Maarten Wegewijs
Keyword(s):  
Time Evolution ◽  
Quantum Dynamics ◽  
Open Systems ◽  
Broad Class ◽  
Open Quantum Systems ◽  
Causal Structure ◽  
Wide Band ◽  
Quantum Systems ◽  
Strong Interactions ◽  
General Symmetry

We consider the exact time-evolution of a broad class of fermionic open quantum systems with both strong interactions and strong coupling to wide-band reservoirs. We present a nontrivial fermionic duality relation between the evolution of states (Schrödinger) and of observables (Heisenberg). We show how this highly nonintuitive relation can be understood and exploited in analytical calculations within all canonical approaches to quantum dynamics, covering Kraus measurement operators, the Choi-Jamiołkowski state, time-convolution and convolutionless quantum master equations and generalized Lindblad jump operators. We discuss the insights this offers into the divisibility and causal structure of the dynamics and the application to nonperturbative Markov approximations and their initial-slip corrections. Our results underscore that predictions for fermionic models are already fixed by fundamental principles to a much greater extent than previously thought.

scholarly journals Complex Time Evolution of Open Quantum Systems

2011 ◽  
Vol 18 (03) ◽  
pp. 261-288
Author(s):  
C. N. Gagatsos ◽  
A. I. Karanikas ◽  
G. I. Kordas
Keyword(s):  
Time Evolution ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Compact Representation ◽  
Complex Time ◽  
Open Quantum ◽  
Time Formalism ◽  
Technical Details ◽  
Set Up ◽  
Reduced Density

We combine, in a single set-up, complex time parametrization in path integration, and closed time formalism of non-equilibrium field theories to produce a compact representation of time evolution of the reduced density matrix. In this framework we introduce a cluster-type expansion that facilitates perturbative and non-petrurbative calculations in the realm of open quantum systems. The technical details of some very simple examples are discussed.

scholarly journals An Invitation to Quantum Channels

Quanta ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 54 ◽  
Author(s):  
Vinayak Jagadish ◽  
Francesco Petruccione
Keyword(s):  
Time Evolution ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Active Area ◽  
Quantum Channels ◽  
Open Quantum ◽  
Potential Applications

Open quantum systems have become an active area of research, owing to its potential applications in many different fields ranging from computation to biology. Here, we review the formalism of dynamical maps used to represent the time evolution of open quantum systems and discuss the various representations and properties of the same, with many examples.Quanta 2018; 7: 54–67.

scholarly journals On non-Markovian Time Evolution in Open Quantum Systems

2007 ◽  
Vol 14 (03) ◽  
pp. 265-274 ◽  
Author(s):  
Andrzej Kossakowski ◽  
Rolando Rebolledo
Keyword(s):  
Time Evolution ◽  
Open System ◽  
Open Quantum Systems ◽  
Vacuum State ◽  
Quantum Systems ◽  
Initial State ◽  
Completely Positive ◽  
Open Quantum

Non-Markovian reduced dynamics of an open system is investigated. In the case when the initial state of the reservoir is the vacuum state, an approximation is introduced which makes it possible to construct a reduced dynamics which is completely positive.

Particle populations and number operators in quantum theory

1972 ◽  
Vol 4 (01) ◽  
pp. 39-80 ◽  
Author(s):  
J. E. Moyal
Keyword(s):  
Statistical Theory ◽  
Quantum Theory ◽  
Subsequent Development ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Subsequent Work ◽  
Von Neumann ◽  
Quantum Mechanical Representation ◽  
Finite Particle ◽  
Number Of Particles

The purpose of the present paper is to give a general theory of the quantum mechanical representation of particle populations.The first part of the paper, Sections 1 to 5, is devoted to a review of mathematical principles of quantum theory, with particular emphasis on the role played by probability concepts, using an approach adapted to the subsequent development of the theory of particle populations. This approach, which goes back in its essentials to von Neumann [20], leans heavily on the subsequent work of Wigner, Mackey, Jauch, Segal, Wightman and many others (see e.g., Mackey [15], Jauch [11], Streater and Wightman [26]). Sections 6 to 9 deal with the representation of finite particle populations: i.e., quantum systems where the total number of particles is an observable. In Section 10 a brief sketch is given of the generalization of the theory to infinite populations where the total number of particles is not an observable, as e.g., in the statistical theory of an infinitely extended gas (see Ruelle [22]). Finally, Section 11 treats some simple examples.

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