Classical Chaos and Quantum Eigenvalues

1988 ◽  
pp. 341-348 ◽  
Author(s):  
M. V. Berry
Keyword(s):  
Classical Chaos

CLASSICAL DIFFUSION AND QUANTAL LOCALIZATION OF A KICKED PARTICLE IN A WELL

1988 ◽  
Vol 02 (01) ◽  
pp. 103-120 ◽  
Author(s):  
AVRAHAM COHEN ◽  
SHMUEL FISHMAN
Keyword(s):  
Diffusion Coefficient ◽  
Classical Limit ◽  
Approximate Formula ◽  
Quantum Systems ◽  
Potential Well ◽  
Diffusive Growth ◽  
Classical Chaos ◽  
The One ◽  
Short Time ◽  
Infinite Potential Well

The classical and quantal behavior of a particle in an infinite potential well, that is periodically kicked is studied. The kicking potential is K|q|α, where q is the coordinate, while K and α are constants. Classically, it is found that for α > 2 the energy of the particle increases diffusively, for α < 2 it is bounded and for α = 2 the result depends on K. An approximate formula for the diffusion coefficient is presented and compared with numerical results. For quantum systems that are chaotic in the classical limit, diffusive growth of energy takes place for a short time and then it is suppressed by quantal effects. For the systems that are studied in this work the origin of the quantal localization in energy is related to the one of classical chaos.

Absence of commensurability in magnetic antidot arrays with classical chaos

1999 ◽  
Vol 60 (16) ◽  
pp. 11535-11539 ◽  
Author(s):  
Ralf Hennig ◽  
Michael Suhrke
Keyword(s):  
Classical Chaos ◽  
Antidot Arrays

scholarly journals Classical Chaos Described by a Density Matrix

Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 739-746
Author(s):  
Andres Mauricio Kowalski ◽  
Angelo Plastino ◽  
Gaspar Gonzalez
Keyword(s):  
Density Matrix ◽  
Pure State ◽  
Classical Limit ◽  
Degrees Of Freedom ◽  
Temporal Evolution ◽  
Entropy Density ◽  
State Density ◽  
Unexpected Result ◽  
Semiclassical Model ◽  
Classical Chaos

In this paper, a reference to the semiclassical model, in which quantum degrees of freedom interact with classical ones, is considered. The classical limit of a maximum-entropy density matrix that describes the temporal evolution of such a system is analyzed. Here, it is analytically shown that, in the classical limit, it is possible to reproduce classical results. An example is classical chaos. This is done by means a pure-state density matrix, a rather unexpected result. It is shown that this is possible only if the quantum part of the system is in a special class of states.

scholarly journals A quantum Rosetta Stone for the information paradox

2014 ◽  
Vol 23 (12) ◽  
pp. 1442013 ◽  
Author(s):  
Leopoldo A. Pando Zayas
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Quantum Chaos ◽  
Black Hole Physics ◽  
Information Loss ◽  
Information Paradox ◽  
Information Loss Paradox ◽  
Conformal Field ◽  
Classical Chaos ◽  
Rosetta Stone

The black hole information loss paradox epitomizes the contradictions between general relativity and quantum field theory. The AdS/conformal field theory (CFT) correspondence provides an implicit answer for the information loss paradox in black hole physics by equating a gravity theory with an explicitly unitary field theory. Gravitational collapse in asymptotically AdS spacetimes is generically turbulent. Given that the mechanism to read out the information about correlations functions in the field theory side is plagued by deterministic classical chaos, we argue that quantum chaos might provide the true Rosetta Stone for answering the information paradox in the context of the AdS/CFT correspondence.

HUN TUN VERSUS BIG BANG: HOW CLASSICAL CHAOS IMPLIES BOTH "THERMODYNAMICS" AND "CRYODYNAMICS"

2012 ◽  
Vol 22 (02) ◽  
pp. 1230007
Author(s):  
OTTO E. RÖSSLER
Keyword(s):  
Chaotic Behavior ◽  
Big Bang ◽  
Geometric Proof ◽  
Ancient China ◽  
Ancient Greek ◽  
Classical Chaos ◽  
History Of ◽  
Hubble’S Law ◽  
Newtonian Systems ◽  
Point Of Departure

The pre-history of chaos in a rationalist context is taken as a point of departure, starting out with ancient China. The related ancient-Greek "unmixing theory" then leads over to two simple formally 2-body Hamiltonian systems exhibiting chaotic behavior. When the two masses involved are unequal, "pseudoattractors" are formed. Deterministic statistical "thermodynamics" with its dissipative behavior arises when the potential is repulsive. Deterministic statistical "cryodynamics" arises when the potential is attractive. The latter class of Newtonian systems is characterized by "antidissipative" behavior. A geometric proof is sketched in the footsteps of Sinai and Bunimovich. Antidissipative behavior is known empirically from Hubble's law which was so far explained in less fundamental terms. Three experimental examples are proposed.

Classical chaos and quantal Wigner distributions for the diamagnetic H atom

1994 ◽  
Vol 189 (1-2) ◽  
pp. 64-71 ◽  
Author(s):  
W. Schweizer ◽  
M. Schaich ◽  
W. Jans ◽  
H. Ruder
Keyword(s):  
Classical Chaos ◽  
Wigner Distributions
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