Time-dependent Chemical Potential Research Articles

Competition of long-range interactions and noise at a ramped quench dynamical quantum phase transition: The case of the long-range pairing Kitaev chain

The nonequilibrium dynamics of long-range pairing Kitaev model with noiseless/noisy linear time dependent chemical potential, is investigated in the framework of dynamical quantum phase transitions (DQPTs). We have shown that for the ramp crossing a single quantum critical point, while the short-range pairing Kitaev model displays a single critical time scale, the long-range pairing induces a region with three DQPTs time scales. We have found that the region with three DQPTs time scales shrinks in the presence of the noise. In addition, we have uncovered that for a quench crossing two critical points, the critical sweep velocity above which the DQPTs disappear enhances by the long-range pairing exponent while decreases in the presence of the noise. On the basis of numerical simulations, we have shown that noise diminishes the long-range pairing inductions. Published by the American Physical Society 2024

Elasto-thermodiffusive interaction subjected to rectangular thermal pulse and time-dependent chemical shock due to Caputo-Fabrizio heat transfer

This present work is devoted to investigate the transient phenomena for a novel mathematical model of elasto-thermodiffusion in an isotropic three-dimensional thermoelastic medium subjected to permeating gas induced by a rectangular thermal pulse, where the heat conduction equation is defined in an integral form of a common derivative involving a nonsingular kernel interval by incorporating the Caputo-Fabrizio (CF) heat transfer law. The time-dependent chemical potential is also assumed to be known on the bounding plane. Employing the Laplace transform and double-Fourier transform techniques, the problem has been solved analytically in the transformed domain. Numerical inversion of the Laplace transform and double-Fourier transforms are carried out using a Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of the CF parameter and thermodiffusion also.

Solving a nonlinear analytical model for bosonic equilibration

An integrable nonlinear model for the time-dependent equilibration of a bosonic system that has been devised earlier is solved exactly with boundary conditions that are appropriate for a truncated Bose-Einstein distribution, and include the singularity at ε=μ. The buildup of a thermal tail during evaporative cooling, as well as the transition to the condensed state are accounted for. To enforce particle-number conservation during the cooling process with an energy-dependent density of states for a three-dimensional thermal cloud, a time-dependent chemical potential is introduced.

Geometric evolution of complex networks with degree correlations.

We present a general class of geometric network growth mechanisms by homogeneous attachment in which the links created at a given time t are distributed homogeneously between a new node and the existing nodes selected uniformly. This is achieved by creating links between nodes uniformly distributed in a homogeneous metric space according to a Fermi-Dirac connection probability with inverse temperature β and general time-dependent chemical potential μ(t). The chemical potential limits the spatial extent of newly created links. Using a hidden variable framework, we obtain an analytical expression for the degree sequence and show that μ(t) can be fixed to yield any given degree distributions, including a scale-free degree distribution. Additionally, we find that depending on the order in which nodes appear in the network-its history-the degree-degree correlations can be tuned to be assortative or disassortative. The effect of the geometry on the structure is investigated through the average clustering coefficient 〈c〉. In the thermodynamic limit, we identify a phase transition between a random regime where 〈c〉→0 when β<β_{c} and a geometric regime where 〈c〉>0 when β>β_{c}.

Kinetic Monte Carlo simulation of nanoparticle film formation via nanocolloid drying

A kinetic Monte Carlo simulation of nanoparticle film formation via nanocolloid drying is presented. The proposed two-dimensional model addresses the dynamics of nanoparticles in the vertical plane of a drying nanocolloid film. The gas–liquid interface movement due to solvent evaporation was controlled by a time-dependent chemical potential, and the resultant particle dynamics including Brownian diffusion and aggregate growth were calculated. Simulations were performed at various Peclet numbers defined based on the rate ratio of solvent evaporation and nanoparticle diffusion. At high Peclet numbers, nanoparticles accumulated at the top layer of the liquid film and eventually formed a skin layer, causing the formation of a particulate film with a densely packed structure. At low Peclet numbers, enhanced particle diffusion led to significant particle aggregation in the bulk colloid, and the resulting film structure became highly porous. The simulated results showed some typical characteristics of a drying nanocolloid that had been reported experimentally. Finally, the potential of the model as well as the remaining challenges are discussed.

Expanding plasmas from anti de Sitter black holes

We introduce a new foliation of AdS$_5$ black holes such that the conformal boundary takes the form of a $4$-dimensional FLRW spacetime with scale factor $a(t)$. The foliation employs Eddington-Finkelstein-like coordinates and is applicable to a large class of AdS black holes, supported by matter fields or not, considerably extending previous efforts in the literature. We argue that the holographic dual picture of a CFT plasma on a FLRW background provides an interesting prototype to study the nonequilibrium dynamics of expanding plasmas and use holographic renormalization to extract the renormalized energy-momentum tensor of the dual plasma. We illustrate the procedure for three black holes of interest, namely AdS-Schwarzschild, AdS-Gauss-Bonnet, and AdS-Reissner-Nordstr\"om. For the latter, as a by-product, we show that the nonequilibrium dynamics of a CFT plasma subject to a quench in the chemical potential (i.e., a time-dependent chemical potential) resembles a cosmological evolution with the scale factor $a(t)$ being inversely related to the quench profile.

Leptogenesis via neutrino production during Higgs condensate relaxation

During inflation, scalar fields, including the Higgs boson, may acquire a nonzero vacuum expectation value, which must later relax to the equilibrium value during reheating. In the presence of the time-dependent condensate, the vacuum state can evolve into a state with a nonzero particle number. We show that, in the presence of lepton number violation in the neutrino sector, the particle production can explain the observed matter-antimatter asymmetry of the universe. We find that this form of leptogenesis is particularly effective when the Higgs condensate decays rapidly and at low reheat scale. As part of the calculation, we present some exact results for the Bogoliubov transformations for Majorana fermions with a nonzero time-dependent chemical potential, in addition to a time-dependent mass.

The enhanced holographic superconductor: is it possible?

It is known that time-dependent perturbations can enhance superconductivity and increase the critical temperature. If this phenomenon happens to high-T_c superconductors, one could obtain room-temperature superconductors, but this is still an open issue experimentally. Meanwhile, we would like to understand this phenomenon from gravity dual and see if the enhancement is possible for holographic superconductors. Previous work (arXiv:1104.4098 [hep-th]) has studied this issue by adding a "time-dependent chemical potential," but their analysis is questionable as a true dynamic equilibrium. In particular, the AdS boundary does not supply energy to the bulk spacetime in their setup. A more appropriate way to discuss the enhancement is to add a time-dependent vector potential, i.e., a time-dependent electric field. However, the enhancement does not occur for holographic superconductors.

ANALYTIC TREATMENT ON STIMULATED HOLOGRAPHIC SUPERCONDUCTORS

Using the classical time-average approximation to deal with equation of motion for scalar field, holographic superconductor with a time-dependent chemical potential is studied analytically in probe limit. On the basis of the minimum eigenvalue of Sturm–Liouville equation, concrete values of the phase transition temperature and critical frequency are obtained. The condensed solution in high frequency regime is also calculated. It is shown that the phase transition temperature enhances and the superconductivity can be got easier as the frequency of the time-dependent chemical potential, which should be larger than the critical frequency, rises.

Time-Dependent Multiconfiguration Theory and Its Application to Ultrafast Electronic Dynamics of Molecules in an Intense Laser Field

(spin-orbitals) as Φ(t )= P I CI (t)ΦI (t). The equations of motion (EOMs) for spin-orbitals in coordinate representation are derived together with the EOMs for configuration interaction coefficients CI (t). As an example of application to molecules, we presented the results of investigation of the ionization dynamics of H2 interacting with a near-infrared intense laser filed. By extending the concept of Hartree-Fock orbital energy to multiconfiguration theory, we newly introduced the molecular orbital of natural spin-orbitals (NSOs) {j} of a many-electron system and defined the orbital potentialsj(t) and correlation energies V c j (t) of NSOs. The total energy E(t) is decomposed into individual components as E(t )= P j ωj(t)¯ � j(t )a s in thermodynamics, whereωj(t) are the occupation numbers of {j} .W e proved that this type of partition of the total energy is interpreted as the time-dependent chemical potential for the two-electron system. The newly defined correlation energy V c j (t) associated with the j th NSO, involved inj(t), reflects dynamical electron correlations on the attosecond timescale. We also compared the energy ζj(t) directly supplied by the applied field with the net energy gain Δ¯ j (t) for respective natural orbitals. The responses of natural orbitals can be classified into three: Δ¯ j (t )= ζj (t) (spectator orbital); Δ¯ j(t) ζ j(t) (energy acceptor orbital). We found that ionization of H2 most efficiently occurs from a time-developing energy acceptor NSO 2σg for the case of the present applied field. We concluded that energy acceptor natural orbitals play a key role in ionization processes.

Analytic Treatment on Stimulated Holographic P-wave Superconductors

Holographic P-wave superconductor with a time-dependent source is investigated analytically in a 4+1 dimensional bulk. The concrete value of critical temperature is produced by calculating the minimum eigenvalue of Sturm-Liouville equation in high frequency regime. The condensed solution is calculated too. It is shown that the phase transition temperature enhances and the condensate superconducts easier as the frequency of the time-dependent chemical potential raises.

Universal time-dependent deformations of Schrödinger geometry

We investigate universal time-dependent exact deformations of Schrodinger geometry. We present 1) scale invariant but non-conformal deformation, 2) non-conformal but scale invariant deformation, and 3) both scale and conformal invariant deformation. All these solutions are universal in the sense that we could embed them in any supergravity constructions of the Schrodinger invariant geometry. We give a field theory interpretation of our time-dependent solutions. In particular, we argue that any time-dependent chemical potential can be treated exactly in our gravity dual approach.

Constraining gravitino dark matter with the cosmic microwave background

We consider super-gravity models in which the lightest supersymmetric particle (LSP) is a stable gravitino. The next-to-lightest supersymmetric particle (NLSP) freezes out with its thermal relic density and then decays after $(10^5-10^{10})$ sec, injecting high-energy photons into the cosmic plasma. These photons heat up the electron plasma which then thermalizes with the cosmic microwave background (CMB) via Compton scattering, bremsstrahlung and double-Compton scattering. Contrary to previous studies which assume instantaneous energy injection, we solve the full kinetic equation for the photon number density with a source term describing the decay of the NLSP. This source term is based on the requirement that the injected energy be almost instantaneously redistributed by Compton scattering, hence leading to a time-dependent chemical potential. We investigate the case of a stau NLSP and determine the constraints on the gravitino and stau masses from observations of the CMB spectrum by assuming that all gravitino LSPs come from stau NLSP decays. Unlike the analytical approximations, we find that there may be a stau mass below which the constraint from the CMB spectrum vanishes.

Relaxation of an electron system: Conserving approximation

The dynamic response of an interacting electron system is determined by an extension of the relaxation-time approximation forced to obey local conservation laws for number, momentum and energy. A consequence of these imposed constraints is that the local electron equilibrium distribution must have a space- and time-dependent chemical potential, drift velocity and temperature. Both quantum kinetic and semi-classical arguments are given, and we calculate and analyze the corresponding analytical d-dimensional dielectric function. Dynamical correlation, arising from relaxation effects, is shown to soften the plasmon dispersion of both two- and three-dimensional systems. Finally, we consider the consequences for a hydrodynamic theory of a d-dimensional interacting electron gas, and by incorporating the competition between relaxation and inertial effects we derive generalised hydrodynamic equations applicable to arbitrary frequencies.