Time evolution of two coupled general driven time-dependent oscillators

1995 ◽  
Vol 110 (9) ◽  
pp. 1015-1024 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Time Evolution ◽  
Time Dependent

scholarly journals The time-dependent angular analysis of Bd → KSℓℓ, a new benchmark for new physics

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Sébastien Descotes-Genon ◽  
Martín Novoa-Brunet ◽  
K. Keri Vos
Keyword(s):  
Time Evolution ◽  
Form Factors ◽  
New Physics ◽  
Time Dependent ◽  
Angular Analysis ◽  
Time Dependent Analysis ◽  
Tensor Operators

Abstract We consider the time-dependent analysis of Bd→ KSℓℓ taking into account the time-evolution of the Bd meson and its mixing into $$ {\overline{B}}_d $$ B ¯ d . We discuss the angular conventions required to define the angular observables in a transparent way with respect to CP conjugation. The inclusion of time evolution allows us to identify six new observables, out of which three could be accessed from a time-dependent tagged analysis. We also show that these observables could be obtained by time-integrated measurements in a hadronic environment if flavour tagging is available. We provide simple and precise predictions for these observables in the SM and in NP models with real contributions to SM and chirally flipped operators, which are independent of form factors and charm-loop contributions. As such, these observables provide robust and powerful cross-checks of the New Physics scenarios currently favoured by global fits to b → sℓℓ data. In addition, we discuss the sensitivity of these observables with respect to NP scenarios involving scalar and tensor operators, or CP-violating phases. We illustrate how these new observables can provide a benchmark to discriminate among the various NP scenarios in b → sμμ. We discuss the extension of these results for Bs decays into f0, η or η′.

scholarly journals Coagulation Processes with Gibbsian Time Evolution

2012 ◽  
Vol 49 (03) ◽  
pp. 612-626
Author(s):  
Boris L. Granovsky ◽  
Alexander V. Kryvoshaev
Keyword(s):  
Stochastic Process ◽  
Recurrence Relation ◽  
Time Evolution ◽  
Nonnegative Function ◽  
Gibbs Distribution ◽  
Time Dependent ◽  
Explicit Solutions ◽  
Gibbs Distributions ◽  
Giant Cluster ◽  
Positive Integers

We prove that a stochastic process of pure coagulation has at any timet≥ 0 a time-dependent Gibbs distribution if and only if the rates ψ(i,j) of single coagulations are of the form ψ(i;j) =if(j) +jf(i), wherefis an arbitrary nonnegative function on the set of positive integers. We also obtain a recurrence relation for weights of these Gibbs distributions that allow us to derive the general form of the solution and the explicit solutions in three particular cases of the functionf. For the three corresponding models, we study the probability of coagulation into one giant cluster by timet> 0.

Critical dynamics and renormalization group (RG)

2021 ◽  
pp. 875-898
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Renormalization Group ◽  
Time Evolution ◽  
Langevin Equation ◽  
Scaling Laws ◽  
Transport Coefficients ◽  
Time Dependent ◽  
Critical Systems ◽  
Static Properties ◽  
Critical Domain ◽  
Dynamical Scaling

Time evolution, near a phase transition in the critical domain of critical systems not far from equilibrium, using a Langevin-type evolution is studied. Typical quantities of interest are relaxation rates towards equilibrium, time-dependent correlation functions and transport coefficients. The main motivation for such a study is that, in systems in which the dynamics is local (on short time-scales, a modification of a dynamic variable has an influence only locally in space) when the correlation length becomes large, a large time-scale emerges, which characterizes the rate of time evolution. This phenomenon called critical slowing down leads to universal behaviour and scaling laws for time-dependent quantities. In contrast with the situation in static critical phenomena, there is no clean and systematic derivation of the dynamical equations governing the time evolution in the critical domain, because often the time evolution is influenced by conservation laws involving the order parameter, or other variables like energy, momentum, angular momentum, currents and so on. Indeed, the equilibrium distribution does not determine the driving force in the Langevin equation, but only the dissipative couplings are generated by the derivative of the equilibrium Hamiltonian, and directly related to the static properties. The purely dissipative Langevin equation specifically discussed, corresponding to static models like the f4 field theory and two-dimensional models. Renormalization group (RG) equations are derived, and dynamical scaling relations established.

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.

scholarly journals LION: A dynamic computer model for the low-latitude ionosphere

2007 ◽  
Vol 25 (11) ◽  
pp. 2371-2392 ◽  
Author(s):  
J. A. Bittencourt ◽  
V. G. Pillat ◽  
P. R. Fagundes ◽  
Y. Sahai ◽  
A. A. Pimenta
Keyword(s):  
Magnetic Field ◽  
Time Evolution ◽  
Computer Model ◽  
Transport Processes ◽  
Time Dependent ◽  
Low Latitude ◽  
Radiation Chemical ◽  
Neutral Winds ◽  
Plasma Drifts ◽  
Low Latitude Ionosphere

Abstract. A realistic fully time-dependent computer model, denominated LION (Low-latitude Ionospheric) model, that simulates the dynamic behavior of the low-latitude ionosphere is presented. The time evolution and spatial distribution of the ionospheric particle densities and velocities are computed by numerically solving the time-dependent, coupled, nonlinear system of continuity and momentum equations for the ions O+, O2+, NO+, N2+ and N+, taking into account photoionization of the atmospheric species by the solar extreme ultraviolet radiation, chemical and ionic production and loss reactions, and plasma transport processes, including the ionospheric effects of thermospheric neutral winds, plasma diffusion and electromagnetic E×B plasma drifts. The Earth's magnetic field is represented by a tilted centered magnetic dipole. This set of coupled nonlinear equations is solved along a given magnetic field line in a Lagrangian frame of reference moving vertically, in the magnetic meridian plane, with the electromagnetic E×B plasma drift velocity. The spatial and time distribution of the thermospheric neutral wind velocities and the pattern of the electromagnetic drifts are taken as known quantities, given through specified analytical or empirical models. The model simulation results are presented in the form of computer-generated color maps and reproduce the typical ionization distribution and time evolution normally observed in the low-latitude ionosphere, including details of the equatorial Appleton anomaly dynamics. The specific effects on the ionosphere due to changes in the thermospheric neutral winds and the electromagnetic plasma drifts can be investigated using different wind and drift models, including the important longitudinal effects associated with magnetic declination dependence and latitudinal separation between geographic and geomagnetic equators. The model runs in a normal personal computer (PC) and generates color maps illustrating the typical behavior of the low-latitude ionosphere for a given longitudinal region, for different seasons, geophysical conditions and solar activity, at each instant of time, showing the time evolution of the low-latitude ionosphere, between about 20° north and south of the magnetic equator. This paper presents a detailed description of the mathematical model and illustrative computer results.

SPIN DYNAMICS OF MOLECULAR MAGNET INTERACTING WITH INJECTED ELECTRONS

2003 ◽  
Vol 17 (07) ◽  
pp. 1117-1125 ◽  
Author(s):  
DONG-SHENG HU ◽  
SHI-JIE XIONG
Keyword(s):  
Exchange Interaction ◽  
Time Evolution ◽  
Electron Spin ◽  
Spin Dynamics ◽  
Molecular Magnets ◽  
Time Dependent ◽  
Molecular Magnet ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Local Spin

We investigate the time evolution of the local spin in a molecular magnet interacting with injected electrons. By solving the time-dependent Schrödinger equations, we find that the variation in the magnetization of the molecular magnet and the electron spin crucially depends on the strength of the exchange interaction. We calculate the time evolution of the entanglement between the injected electron and the molecular magnet. It is found that the entanglement oscillates in time and the oscillations are closely related to the changes in the spins. The study provides an estimation of the feasibility of the encoding and read-out by using the polarization of the molecular magnets and the injected electrons.

WEHRL ENTROPY AND ENTANGLEMENT OF A TIME-DEPENDENT TWO-LEVEL TRAPPED ION INTERACTING WITH A LASER FIELD

2008 ◽  
Vol 06 (02) ◽  
pp. 331-339
Author(s):  
MAHMOUD ABDEL-ATY ◽  
SAYED ABDEL-KHALEK ◽  
ABDEL-SHAFY F. OBADA
Keyword(s):  
Exact Solution ◽  
Time Evolution ◽  
Laser Field ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Heisenberg Equation ◽  
Wehrl Entropy ◽  
Entanglement Generation ◽  
Trapped Ion ◽  
Cat States

The time evolution of the atomic Wehrl entropy and long-lived entanglement generation using a single trapped ion interacting with a laser field are analyzed. Starting from the Heisenberg equation of motion, an exact solution of the system is obtained by indicating that there are some interesting features when a time-dependent modulating function is considered. We demonstrate that the long-living quantum entanglement can be obtained using the time-independent interaction when the field is initially in a pair cat states.

scholarly journals Angular distribution of scission neutrons studied with time-dependent Schrödinger equation

2018 ◽  
Vol 169 ◽  
pp. 00029
Author(s):  
Takahiro Wada ◽  
Tomomasa Asano ◽  
Nicolae Carjan
Keyword(s):  
Wave Function ◽  
Angular Distribution ◽  
Schrödinger Equation ◽  
Time Evolution ◽  
Schrodinger Equation ◽  
Initial Distribution ◽  
Time Dependent ◽  
Heavy Fragment ◽  
Fission Fragments ◽  
Asymmetric Fission

We investigate the angular distribution of scission neutrons taking account of the effects of fission fragments. The time evolution of the wave function of the scission neutron is obtained by integrating the time-dependent Schrodinger equation numerically. The effects of the fission fragments are taken into account by means of the optical potentials. The angular distribution is strongly modified by the presence of the fragments. In the case of asymmetric fission, it is found that the heavy fragment has stronger effects. Dependence on the initial distribution and on the properties of fission fragments is discussed. We also discuss on the treatment of the boundary to avoid artificial reflections

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