scholarly journals Phonon-induced disorder in dynamics of optically pumped metals from nonlinear electron-phonon coupling

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
John Sous ◽  
Benedikt Kloss ◽  
Dante M. Kennes ◽  
David R. Reichman ◽  
Andrew J. Millis
Keyword(s):  
Spatial Coherence ◽  
Initial Time ◽  
Optically Pumped ◽  
Translation Invariant ◽  
Pump Probe ◽  
Equilibrium Dynamics ◽  
Correlated Electron ◽  
Electron Phonon Coupling ◽  
Long Time ◽  
High Transition

AbstractThe non-equilibrium dynamics of matter excited by light may produce electronic phases, such as laser-induced high-transition-temperature superconductivity, that do not exist in equilibrium. Here we simulate the dynamics of a metal driven at initial time by a spatially uniform pump that excites dipole-active vibrational modes which couple nonlinearly to electrons. We provide evidence for rapid loss of spatial coherence, leading to emergent effective disorder in the dynamics, which arises in a system unitarily evolving under a translation-invariant Hamiltonian, and dominates the electronic behavior as the system evolves towards a correlated electron-phonon long-time state, possibly explaining why transient superconductivity is not observed. Our framework provides a basis within which to understand correlation dynamics in current pump-probe experiments of vibrationally coupled electrons, highlight the importance of the evolution of phase coherence, and demonstrate that pumped electron-phonon systems provide a means of realizing dynamically induced disorder in translation-invariant systems.

Applications of the Karhunen-Loève Decomposition to Quantum Dynamical Problems

2002 ◽  
Vol 216 (3) ◽  
Author(s):  
H. Dietz ◽  
M. Marek ◽  
A.F. Münster ◽  
V. Engel
Keyword(s):  
Bound State ◽  
Efficient Tool ◽  
Straightforward Manner ◽  
Time Resolved ◽  
Pump Probe ◽  
One Dimensional ◽  
Quantum Dynamical ◽  
Arbitrary Complex ◽  
Long Time ◽  
Complex Valued

The Karhunen-Loève (KL)-decomposition is a standard method to analyze spatiotemporal patterns which are characteristic for non-linear chemical dynamics on surfaces. We apply the KL-decomposition to quantum dynamical problems. Using a variational principle it is shown how to arrive at the KL-expansion of an arbitrary complex valued function. In the case of an one-dimensional bound state motion, the KL-decomposition yields the eigenstates of the system in a straightforward manner. The time-resolved spectroscopy of an atom-molecule collision serves as another application. We demonstrate that the orthonormal decomposition into KL-modes provides an efficient tool to calculate long-time pump-probe signals.

Pump-probe spectrum in a correlated electron-hole system

1998 ◽  
Vol 76-77 ◽  
pp. 79-82
Author(s):  
Takeshi Inagaki ◽  
Masaki Aihara
Keyword(s):  
Electron Hole ◽  
Pump Probe ◽  
Correlated Electron

Linear processes in stably and unstably stratified rotating turbulence

2002 ◽  
Vol 465 ◽  
pp. 157-190 ◽  
Author(s):  
H. HANAZAKI
Keyword(s):  
Kinetic Energy ◽  
Time Development ◽  
Initial Time ◽  
Small Scale ◽  
Coriolis Parameter ◽  
Linear Processes ◽  
Time Asymptotics ◽  
Rotating Turbulence ◽  
Long Time ◽  
Energy Components

Unsteady turbulence in stably and unstably stratified flow with system rotation around the vertical axis is analysed using the rapid distortion theory (RDT). Complete linear solutions for the spectra, variances and covariances are obtained analytically, and their characteristics, including the short- and long-time asymptotics and the effect of initial conditions, are examined in detail. It has been found that the rotation modifies the energy partition among the three kinetic energy components and the potential energy, and the ratio of the Coriolis parameter f to the Brunt–Väisälä frequency N, i.e. f/N, determines the final steady values of these components. The ratio also determines the phase of the energy/flux oscillation. Depending on whether f/N > 1 or f/N < 1, there is a phase shift of ±π/4. However, unsteady aspects are largely dominated by stratification. This occurs because the effects of the Coriolis parameter f appear only in the form of fk3, which vanishes for the horizontal wavenumber components (k3 = 0), which contribute most to the energies and the fluxes. For example, the oscillation frequency of the energies and the fluxes asymptotes to 2N over a long time, in agreement with the stratified non-rotating turbulence. The initial time development is also dominanted by the stratification, and the short-time asymptotics (Nt, ft [Lt ] 1) agree with those for non-rotating stratified fluids in the lowest-order approximation. In the special case of f = N, all the wavenumber components oscillate in phase, leading to no inviscid decay of oscillation. This is in contrast to the general case of f ≠ N, in which inviscid decay has been observed. For pure rotation (f ≠ 0, N = 0), analytical solutions showed that any turbulence that is initially axisymmetric around the rotation axis recovers exact three-dimensional isotropy in the kinetic energy components. Comparison with previous DNS and experiments shows that many of the unsteady aspects of the kinetic and potential energies and the vertical density flux can be explained by the linear processes described by RDT. Even the time development of the vertical vorticity, which would represent the small-scale characteristics of turbulence, agrees well with DNS. For unstably stratified turbulence, the initial processes observed in DNS and experiments, such as the initial decay of the kinetic energy due to viscosity and the subsequent rapid growth of the vertical kinetic energy compared to the horizontal kinetic energy, could be explained by RDT.

scholarly journals Asymptotics for the long-time evolution of kurtosis of narrow-band ocean waves

2018 ◽  
Vol 859 ◽  
pp. 790-818 ◽  
Author(s):  
Peter A. E. M. Janssen ◽  
Augustus J. E. M. Janssen
Keyword(s):  
Analytical Solution ◽  
Extreme Events ◽  
Narrow Band ◽  
Wave Train ◽  
Ocean Waves ◽  
Initial Time ◽  
Nls Equation ◽  
Excess Kurtosis ◽  
Long Time ◽  
Nonlinear Focusing

In this paper we highlight that extreme events such as freak waves are a transient phenomenon in keeping with the old fisherman tale that these extreme events seem to appear out of nowhere. Janssen (J. Phys. Oceanogr., vol. 33, 2003, pp. 863–884) obtained an evolution equation for the ensemble average of the excess kurtosis, which is a measure for the deviation from normality and an indicator for nonlinear focusing resulting in extreme events. In the limit of a narrow-band wave train, whose dynamics is governed by the two-dimensional nonlinear Schrödinger (NLS) equation, the excess kurtosis is under certain conditions seen to grow to a maximum after which it decays to zero for large times. This follows from a numerical solution of the problem and also from an analytical solution presented by Fedele (J. Fluid Mech., vol. 782, 2015, pp. 25–36). The analytical solution is not explicit because it involves an integral from initial time to actual time. We therefore study a number of properties of the integral expression in order to better understand some interesting features of the time-dependent excess kurtosis and the generation of extreme events.

scholarly journals Mathematical model study of a pandemic: Graded lockdown approach

2020 ◽  
Author(s):  
S Chateerjee ◽  
V.C. Vani ◽  
Ravinder Banyal
Keyword(s):  
Time Scale ◽  
Total Population ◽  
Formal Solution ◽  
Initial Time ◽  
Illustrative Case ◽  
Susceptible Individual ◽  
Urban Centers ◽  
Model Study ◽  
Long Time ◽  
Type Differential Equation

A kinetic approach is developed, in a "tutorial style" to describe the evolution of an epidemic with spread taking place through contact. The "infection-rate" is calculated from the rate at which an infected person approaches an uninfected susceptible individual, i.e. a potential recipient of the disease, up to a distance p, where the value of p may lie between pmin≤p≤pmax. We consider a situation with a total population of N individuals, living in an area A, x(t) amongst them being infected while xd(t) = β′x(t) is the number that has died in the course of transmission and evolution of the epidemic. The evolution is developed under the conditions (1) a faction α(t) of the [N-x(t)−xd(t)] uninfected individuals and (2) a β(t) fraction of the x(t) infected population are quarantined, while the "source-events" that spread the infection are considered to occur with frequency υ. The processes of contact and transmission are considered to be Markovian. Transmission is assumed to be inhibited by several processes like the use of "masks", "hand washing or use of sanitizers" while "physical distancing" is described by p. The evolution equation for x(t) is a Riccati - type differential equation whose coefficients are time-dependent quantities, being determined by an interplay between the above parameters. A formal solution for x(t) is presented, for a "graded lockdown" with the parameters, 0≤α(t), β(t)≤1 reaching their respective saturation values in time scales, τ1, τ2 respectively, from their initial values α(0)=β(0)=0. The growth is predicted for several BBMP wards in Bengaluru and in urban centers in Chikkaballapur district, as an illustrative case. The above selections serve as model cases for high, moderate and thin population densities. It is seen that the evolution of [x(t)/N] with time depends upon (a) the initial time scale of evolution, (b) the time scale of cure and (c) on the time dependence of the Lockdown function Q(t) = {[1−α(t)]·[1−β(t)]}. The formulae are amenable to simple computations and show that in order to curb the spread one must ensure that Q(∞) must be below a critical value and the vigilance has to be continued for a long time (at least 100 to 150 days) after the decay starts,to avoid all chances of the infection reappearing.

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