Quantum Systems and Finite Approximations

10.1142/9740 ◽  
2023 ◽  
Author(s):  
Trond Digernes ◽  
Erik Makino Bakken
Keyword(s):  
Quantum Systems ◽  
Finite Approximations

scholarly journals Brownian motion and finite approximations of quantum systems over local fields

2017 ◽  
Vol 29 (05) ◽  
pp. 1750016 ◽  
Author(s):  
Erik Makino Bakken ◽  
Trond Digernes ◽  
David Weisbart
Keyword(s):  
Brownian Motion ◽  
Random Walks ◽  
Local Field ◽  
Schrödinger Operators ◽  
Quantum Systems ◽  
Local Fields ◽  
Schrodinger Operators ◽  
Finite Systems ◽  
Finite Approximations ◽  
Finite Approximability

We give a stochastic proof of the finite approximability of a class of Schrödinger operators over a local field, thereby completing a program of establishing in a non-Archimedean setting corresponding results and methods from the Archimedean (real) setting. A key ingredient of our proof is to show that Brownian motion over a local field can be obtained as a limit of random walks over finite grids. Also, we prove a Feynman–Kac formula for the finite systems, and show that the propagator at the finite level converges to the propagator at the infinite level.

FINITE APPROXIMATIONS TO QUANTUM SYSTEMS

1994 ◽  
Vol 06 (04) ◽  
pp. 621-648 ◽  
Author(s):  
TROND DIGERNES ◽  
V. S. VARADARAJAN ◽  
S. R. S. VARADHAN
Keyword(s):  
Quantum Systems ◽  
Finite Approximations

Dynamics of One-Dimensional Quantum Systems

2009 ◽  
Author(s):  
Yoshio Kuramoto ◽  
Yusuke Kato
Keyword(s):  
Quantum Systems ◽  
One Dimensional

Coherent population trapping in quantum systems

1993 ◽  
Vol 163 (9) ◽  
pp. 1 ◽  
Author(s):  
B.D. Agap'ev ◽  
M.B. Gornyi ◽  
B.G. Matisov ◽  
Yu.V. Rozhdestvenskii
Keyword(s):  
Quantum Systems ◽  
Coherent Population Trapping ◽  
Population Trapping

Relaxation of interacting open quantum systems

2018 ◽  
Vol 189 (05) ◽  
Author(s):  
Vladislav Yu. Shishkov ◽  
Evgenii S. Andrianov ◽  
Aleksandr A. Pukhov ◽  
Aleksei P. Vinogradov ◽  
A.A. Lisyansky
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

Time evolution of chaotic quantum systems

1992 ◽  
Vol 219 (2) ◽  
pp. 364
Keyword(s):  
Time Evolution ◽  
Quantum Systems

scholarly journals Coarse-grained belief propagation for simulation of interacting quantum systems at all temperatures

2010 ◽  
Vol 81 (5) ◽  
Author(s):  
Ersen Bilgin ◽  
David Poulin
Keyword(s):  
Belief Propagation ◽  
Quantum Systems ◽  
Coarse Grained

scholarly journals -fold supersymmetry in quantum systems with position-dependent mass

2005 ◽  
Vol 39 (1) ◽  
pp. 219-234 ◽  
Author(s):  
Toshiaki Tanaka
Keyword(s):  
Quantum Systems ◽  
Dependent Mass ◽  
Position Dependent Mass
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