scholarly journals Quantum dynamics in a cubic potential in the semi-classical limit: Smearing of the homoclinic bifurcation

Physics Open ◽  
2020 ◽  
pp. 100047
Author(s):  
Akshay Pal ◽  
Jayanta K. Bhattacharjee
Keyword(s):  
Classical Limit ◽  
Quantum Dynamics ◽  
Homoclinic Bifurcation

scholarly journals Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 684
Author(s):  
Giovani Morales-Hernández ◽  
Juan Castellanos ◽  
José Romero ◽  
Andrei Klimov
Keyword(s):  
Classical Limit ◽  
Quantum Dynamics ◽  
Asymptotic Form ◽  
Star Product ◽  
Spin Systems ◽  
Classical Dynamics ◽  
Classical Dynamic ◽  
Variable Spin ◽  
Long Time ◽  
Dynamic Variables

We apply the semi-classical limit of the generalized SO(3) map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on T*S2. Using the asymptotic form of the star-product, we manage to “quantize” one of the classical dynamic variables and introduce a discretized version of the Truncated Wigner Approximation (TWA). Two emblematic examples of quantum dynamics (rotor in an external field and two coupled spins) are analyzed, and the results of exact, continuous, and discretized versions of TWA are compared.

scholarly journals A COLD-ATOM RATCHET INTERPOLATING BETWEEN CLASSICAL AND QUANTUM DYNAMICS

2013 ◽  
Vol 12 (02) ◽  
pp. 1340003 ◽  
Author(s):  
R. K. SHRESTHA ◽  
W. K. LAM ◽  
J. NI ◽  
G. S. SUMMY
Keyword(s):  
Classical Limit ◽  
Quantum Dynamics ◽  
Cold Atom ◽  
Einstein Condensate ◽  
Single Variable ◽  
Pulse Period ◽  
Short Pulses ◽  
Bose Einstein Condensate ◽  
Experimental Parameters ◽  
Bose Einstein

We use an atomic ratchet realized by applying short pulses of an optical standing-wave to a Bose–Einstein condensate to study the crossover between classical and quantum dynamics. The signature of the ratchet is the existence of a directed current of atoms, even though there is an absence of a net bias force. Provided that the pulse period is close to one of the resonances of the system, the ratchet behavior can be understood using a classical like theory which depends on a single variable containing many of the experimental parameters. Here we show that this theory is valid in both the true classical limit, when the pulse period is close to zero, as well as regimes when this period is close to other resonances where the usual scaled Planck's constant is nonzero. By smoothly changing the pulse period between these resonances we demonstrate how it is possible to tune the ratchet between quantum and classical types of behavior.

scholarly journals DUALISM BETWEEN PHYSICAL FRAMES AND TIME IN QUANTUM GRAVITY

2004 ◽  
Vol 19 (20) ◽  
pp. 1519-1527 ◽  
Author(s):  
SIMONE MERCURI ◽  
GIOVANNI MONTANI
Keyword(s):  
Quantum Gravity ◽  
Reference Frame ◽  
Path Integral ◽  
Classical Limit ◽  
Quantum Dynamics ◽  
Einstein Equations ◽  
Quantum Level ◽  
Dust Fluid ◽  
Lapse Function ◽  
Canonical Quantum

In this work we present a discussion of the existing links between the procedures of endowing the quantum gravity with a real time and of including in the theory a physical reference frame. More precisely, as a first step, we develop the canonical quantum dynamics, starting from the Einstein equations in presence of a dust fluid and arrive at a Schrödinger evolution. Then, by fixing the lapse function in the path-integral of gravity, we get a Schrödinger quantum dynamics, of which eigenvalues problem provides the appearance of a dust fluid in the classical limit. The main issue of our analysis is to claim that a theory, in which the time displacement invariance, on a quantum level, is broken, is indistinguishable from a theory for which this symmetry holds, but a real reference fluid is included.

GEOMETRY IN QUANTUM NON-INTEGRABILITY

1993 ◽  
Vol 08 (15) ◽  
pp. 1417-1425 ◽  
Author(s):  
WEI-MIN ZHANG ◽  
DA HSUAN FENG
Keyword(s):  
Classical Limit ◽  
Quantum Correlation ◽  
Quantum Dynamics ◽  
Topological Index ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Compact Case ◽  
Classical Behavior ◽  
Compact Geometry ◽  
Arbitrary Quantum

We present a framework within which the way classical behavior emerges from arbitrary quantum dynamics can be studied systematically. This behavior is characterized by a quenching (topological) index Ξ, which controls the quenching of quantum correlations and signals the existence or the lack of classical limit. The compactness of geometry distinguishes two classes of quantum systems. The kick examples given in this letter suggest that quantum correlation suppresses chaos for compact geometry, while the opposite is found in the non-compact case.

II. Non adiabatic theory of collisions in a radiative field. Semi-classical limit : Ar + O case

1989 ◽  
Vol 50 (10) ◽  
pp. 1195-1208 ◽  
Author(s):  
A. Spielfiedel ◽  
E. Roueff ◽  
N. Feautrier
Keyword(s):  
Classical Limit ◽  
Adiabatic Theory

Non adiabatic theory of collisions in a radiative field. Semi-classical limit

1988 ◽  
Vol 49 (11) ◽  
pp. 1911-1923 ◽  
Author(s):  
N. Feautrier ◽  
E. Roueff ◽  
A. Spielfiedel
Keyword(s):  
Classical Limit ◽  
Adiabatic Theory
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