Weak Coupling Approximation Research Articles

Irreversible Boltzmann samplers in dense liquids: Weak-coupling approximation and mode-coupling theory.

Exerting a nonequilibrium drive on an otherwise equilibrium Langevin process brings the dynamics out of equilibrium but can also speed up the approach to the Boltzmann steady state. Transverse forces are a minimal framework to achieve dynamical acceleration of the Boltzmann sampling. We consider a simple liquid in three space dimensions subjected to additional transverse pairwise forces, and quantify the extent to which transverse forces accelerate the dynamics. We first explore the dynamics of a tracer in a weak coupling regime describing high temperatures. The resulting acceleration is correlated with a monotonous increase of the magnitude of odd transport coefficients (mobility and diffusivity) with the amplitude of the transverse drive. We then develop a nonequilibrium version of the mode-coupling theory able to capture the effect of transverse forces, and more generally of forces created by additional degrees of freedom. Based on an analysis of transport coefficients, both odd and longitudinal, both for the collective modes and for a tracer particle, we find a systematic acceleration of the dynamics. Quantitatively, the gain, which is guaranteed throughout the ergodic phase, turns out to be a decreasing function of temperature beyond a temperature crossover, in particular as the glass transition is approached. Our theoretical results are in good agreement with available numerical results.

A coupled-mode analysis of mode localization on weakly-coupled silicon micromechanical resonators with damping

Mode localization on weakly-coupled silicon resonators in the areas of microelectromechanical systems (MEMS) has been widely studied for highly sensitive sensors of physical and chemical parameter monitoring. In terms of its operation principle, i.e., energy conservation, a system for the weakly-coupled silicon resonator is required to have no damping. In fact, however, various types of energy dissipation mechanisms inevitably lead to the damping even under high vacuum packaging, and for mass sensing scenarios it always operates in high damping environments. The effect of damping on the amplitude and frequency of the weakly-coupled silicon resonator is generally explored by numerical methods. Based on a weak coupling approximation, this article has developed a coupled-mode model for analytically analyzing the effects. A pair of electrostatically-coupled silicon resonator were experimentally fabricated and operated through capacitive transduction. The theoretical and experimental results show a quantitative consistency. The results presented here suggest that it may guide the design of sensors based on mode localization in the presence of damping.

Recovering Complete Positivity of Non-Markovian Quantum Dynamics with Choi-Proximity Regularization

A relevant problem in the theory of open quantum systems is the lack of complete positivity of dynamical maps obtained after weak-coupling approximations, a famous example being the Redfield master equation. A number of approaches exist to recover well-defined evolutions under additional Markovian assumptions, but much less is known beyond this regime. Here, we propose a numerical method to cure the complete-positivity violation issue while preserving the non-Markovian features of an arbitrary original dynamical map. The idea is to replace its unphysical Choi operator with its closest physical one, mimicking recent work on quantum process tomography. We also show that the regularized dynamics is more accurate in terms of reproducing the exact dynamics, which allows us to heuristically push the utilization of these master equations in moderate coupling regimes, where the loss of positivity can have a relevant impact. Published by the American Physical Society 2024

Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach.

Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.

Kerr black hole shadows from axion-photon coupling

We have investigated the motion for photons in the Kerr black hole spacetime under the axion-photon coupling. The birefringence phenomena arising from the axion-photon coupling can be negligible in the weak coupling approximation because the leading-order contributions to the equations of motion come from the square term of the coupling parameter. We find that the coupling parameter makes the size of shadows slightly increase for arbitrary spin parameter. For the rapid rotating black hole case with a larger coupling, we find that there exist a “pedicel”-like structure appeared in the left of the “D”-type like shadows. Comparing the shadow size of the Kerr black hole with the shadow size of the Sgr A* and M87* black holes, we make constraints on the parameter space for such a theoretical model of the axion-photon coupling.

Heat distribution in quantum Brownian motion.

We investigate the heat statistics in a relaxation process of quantum Brownian motion described by the Caldeira-Leggett model. By employing the normal mode transformation and the phase-space formulation approach, we can analyze the quantum heat distribution within an exactly dynamical framework beyond the traditional paradigm of Born-Markovian and weak-coupling approximations. It is revealed that the exchange fluctuation theorem for quantum heat generally breaks down in the strongly non-Markovian regime. Our results may improve the understanding about the nonequilibrium thermodynamics of open quantum systems when the usual Markovian treatment is no longer appropriate.

Generalized uncertainty relation between thermodynamic variables in quantum thermodynamics

Macroscopic thermodynamics, via the weak coupling approximation, assumes that the equilibrium properties of a system are not affected by interactions with its environment. However, this assumption may not hold for quantum systems, where the strength of interaction between the system and the environment may become non-negligible in a strong coupling regime. In such a regime, the equilibrium properties of the system depend on the interaction energy and the system state is no longer of the Gibbs form. Regarding such interactions, using tools from the quantum estimation theory, we derive the thermodynamic uncertainty relation between intensive and extensive variables valid at all coupling regimes through the generalized Gibbs ensemble. Where we demonstrate the lower bound on the uncertainty of intensive variables increases in presence of quantum fluctuations. Also, we calculate the general uncertainty relations for several ensembles to corroborate the literature results, thus showing the versatility of our method.

Shadow revisiting and weak gravitational lensing with Chern-Simons modification

Dynamical Chern-Simons (dCS) gravity has been attracting plenty of attentions due to the fact that it is a parity-violating modified theory of gravity that corresponds to a well-posed effective field theory in weak coupling approximation. In particular, a rotating black hole in dCS gravity is in contrast to the general relativistic counterparts. In this paper, we revisit the shadow of analytical rotating black hole spacetime in dCS modified gravity, based on which we study the shadow observables, discuss the constraint on the model parameters from the Event Horizon Telescope (EHT) observations, and analyze the real part of quasi-normal modes (QNMs) in the eikonal limit. In addition, we explore the deflection angle in weak gravitational field limit with the use of Gauss-Bonnet theorem. We find that the shadow related physics and the weak gravitational lensing effect are significantly influenced by the CS coupling, which could provide theoretical predictions for a future test of the dCS theory with EHT observations.

Level scheme study of Mo91 : Weak-coupling approximation in the N=50 region

The level scheme of $^{91}\mathrm{Mo}$ has been studied using the GALILEO $\ensuremath{\gamma}$-ray spectrometer at Laboratori Nazionali di Legnaro, INFN. Five transitions together with four levels are identified for the first time by the $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence measurement, considerably enriching the negative band in $^{91}\mathrm{Mo}$. The discrepancy in the previous parity assignments for the states higher than 3807.5 keV has been clarified with the help of new experimental results. A shell-model calculation employing the JUN45 interaction is performed in order to get a further understanding of the level structure of $^{91}\mathrm{Mo}$. Being close to $N=50$ shell closure, the weak-coupling approximation between the valence ${g}_{9/2}$ neutron-hole with the even-even core $(^{92}\mathrm{Mo})$ is discussed in $^{91}\mathrm{Mo}$.

Enhancing quantum exchanges between two oscillators

We explore the extent to which two quantum oscillators can exchange their quantum states efficiently through a three-level system which can be spin levels of colored centers in solids. High transition probabilities are obtained using Hamiltonian engineering and quantum control techniques. Starting from a weak coupling approximation, we derive conditions on the spin-oscillator interaction Hamiltonian that enable a high fidelity exhange of quanta. We find that these conditions cannot be fulfilled for arbitrary spin-oscillator coupling. To overcome this limitation, we illustrate how a time-dependent control field applied to the three-level system can lead to an effective dynamic that performs the desired exchange of excitation. In the strong coupling regime, an important loss of fidelity is induced by the dispersion of the excitation onto many Fock states of the oscillators. We show that this detrimental effect can be substantially reduced by suitable control fields, which are computed with optimal control numerical algorithms.

Nonlinear non-Hermitian Landau–Zener–Stückelberg–Majorana interferometry

In this work, we have studied the non-Hermitian nonlinear Landau–Zener–Stückelberg–Majorana (LZSM) interferometry in a non-Hermitian N-body interacting boson system in which the non-Hermiticity is from the nonreciprocal tunnelings between the bosons. By using the mean-field approximation and projective Hilbert space, the effect of nonreciprocity and nonlinearity on the energy spectrum, the dynamics, and the formation of the interference fringes have been studied. The different symmetries and the impact of the two different types of reciprocity, i.e. the in-phase tunneling and anti-phase tunneling, on the energy spectrum and the phase transition between the Josephson oscillations and the self-trapping have been investigated. For the LZSM interferometry, the strength of the nonreciprocity is found to take an essential role in the population of the projective state and the strengths of the interference patterns in the projective space. While the conditions of destructive and constructive interference under the weak-coupling approximation still only depend on the strength of nonlinearity. Our result provides an application of the nonlinear non-Hermitian LZSM interferometry in studying the parameters of a two-level system which related to the nonlinearity and the non-Hermiticity.

Sign of the Feynman propagator and irreversibility

For the interacting Feynman propagator [Formula: see text] of scalar electrodynamics, we show that the sign property, [Formula: see text], may hinge on the reversibility of time evolution. In contrast, [Formula: see text] is indeterminate. When we switch to reduced dynamics under the weak coupling approximation, the positive semidefinite sign of [Formula: see text] is generally lost, unless we impose severe restrictions on the Kraus operators that govern time evolution. With another approximation, the rotating wave approximation, we may recover the sign by restricting the test functions to exponentials under certain conditions.

Entanglement harvesting of inertially moving Unruh-DeWitt detectors in Minkowski spacetime

We investigate the effects of relative motion on entanglement harvesting by considering a pair of Unruh-Dewitt detectors moving at arbitrary but independent and constant velocities, both linearly interacting with a massless scalar field vacuum in four-dimensional Minkowski spacetime. Working within the weak coupling approximation, we find that the negativity is a (nonelementary) function of the relative velocity of the detectors, as well as their energy gaps and minimal separation. We find parameter regions where negativity increases with velocity up to a maximum and then decreases, reaching zero at some sublight velocity. At any given relative velocity, the harvested entanglement is inversely correlated with the detector energy gap (at sufficiently high values) and the distance of closest approach of two detectors.

Role of Rabi oscillations in radiative states due to the fully absorbing smaller plasmonic nanoparticles

The modified radiative and non-radiative states due to the weak coupling of an emitter with other resonant objects (Purcell effect) can be recast as a quantum interference of the paths of the photon that define the classical scattering and absorption by the object. When the coupling is stronger, additional paths representing the Rabi oscillations or the possible re-absorption of the photon from the excited object, by the emitter at the ground-state, have to be included in the quantum interference. The effect of these additional Rabi paths of the photon on the radiative states and the efficiency of spontaneous emission can be approximated using a simple one-loop correction to the weak-coupling approximation. This effect is especially evident in the anomalous enhancements of emission due to extremely small non-scattering (or almost fully absorbing) metal nanoparticles less than 10 nm in dimensions approximately. Extending these corrections to a collective model of spontaneous emission that includes multiple emitters and such very small metal nanoparticles coupled to each other, the large contribution of Rabi paths to radiative decay in such bulk materials is elucidated.

Hamiltonian of mean force in the weak-coupling and high-temperature approximations and refined quantum master equations

The Hamiltonian of mean force is a widely used concept to describe the modification of the usual canonical Gibbs state for a quantum system whose coupling strength with the thermal bath is non-negligible. Here, we perturbatively derive general approximate expressions for the Hamiltonians of mean force in the weak-coupling approximation and in the high-temperature one. We numerically analyze the accuracy of the corresponding expressions and show that the precision of the Bloch–Redfield equantum master equation can be improved if we replace the original system Hamiltonian by the Hamiltonian of mean force.

Median-point approximation and its application for the study of fermionic systems

We consider a system of fermions with local interactions on a lattice (Hubbard model) and apply a novel extension of the Laplace's method (saddle-point approximation) for evaluating the corresponding partition function. There, we introduce dual free bosonic fields, with a propagator corresponding to an effective (renormalized) interaction with Maki-Thompson and Aslamazov-Larkin type corrections and beyond, and demonstrate that the superconducting pairing originates as an instability of the effective interaction. We derive the corresponding Bethe-Salpeter equation (instability criterion) and show that the interaction enters the equation only in its effective form to all orders, including the exchange part of the self-energy. An important implication of this result is that the effective interaction always remains finite, even at phase-transition points, directly contradicting the often used assumption of linear relationship between the interaction and susceptibility, established within the random-phase approximation. By analyzing the Bethe-Salpeter equation in the context of unconventional superconductivity, we find that the presence of a flat band close the Fermi level, found in materials such as twisted bilayer graphene, has a twofold favorable impact persisting beyond the weak-coupling approximation: a reduced kinetic energy cost of the gap formation and an increased anisotropy of the effective interaction, favoring a momentum dependent order parameter.

Dilution of Reactive Plumes: Evolution of Concentration Statistics Under Diffusion and Nonlinear Reaction

Concentration fields of solutes in porous media often exhibit large fluctuations, driven by physical and chemical heterogeneity from the pore to the Darcy scale. For many applications, ranging from reactive transport modeling to toxicology, the knowledge of mean concentrations is not sufficient, and quantifying concentration variability is necessary. The probability density function (PDF) of concentration quantifies the frequency of occurrence of concentration values throughout a spatial domain. While evolution equations and analytical solutions for the concentration PDF exist for conservative solutes, less is known about its evolution under the joint action of transport and reaction. In this work, we investigate how dilution of a reactive plume by diffusion affects the statistics of concentrations. While mixing has no effect on first-order reactions, its coupling with nonlinear reactions leads to non-trivial effective kinetics relevant for a broad range of reactive transport problems. We study the evolution of the concentration PDF under diffusion and nonlinear reaction in one spatial dimension, which represents a critical step toward further coupling with heterogeneous advection. We show that the dependence of the scalar dissipation rate on concentration encodes the impact of diffusive transport on the concentration PDF and derive a dynamical equation for its time evolution. Using a weak-coupling approximation for the reaction and diffusion dynamics, we derive analytical predictions for the concentration PDF and its moments. Our results provide new insights into how diffusion and reaction control concentration variability and open new opportunities for coupling mixing models with chemical reactions.

Coupled Hubbard ladders at weak coupling: Pairing and spin excitations

The Hubbard model provides a simple framework in which one can study how certain aspects of the electronic structure of strongly interacting systems can be tuned to optimize the superconducting pairing correlations and how these changes affect the mechanisms giving rise to them. Here we use a weak-coupling random phase approximation to study a two-dimensional Hubbard model with a unidirectional modulation of the hopping amplitudes as the system evolves from the uniform square lattice to an array of weakly coupled two-leg ladders. We find that the pairing correlations retain their dominant $d_{x^2-y^2}$-wave like structure and that they are significantly enhanced for a slightly modulated lattice. This enhancement is traced backed to an increase in the strength of the spin-fluctuation pairing interacting due to favorable Fermi surface nesting in the modulated system. We then use a random-phase approximation BCS framework to examine the evolution of the neutron resonance in the superconducting state. We find that it changes only weakly for moderate modulations, but breaks up into two distinct resonances at incommensurate wave-vectors in the limit of weakly coupled ladders.

Single-impurity Anderson model out of equilibrium: A two-particle semianalytic approach

We apply a two-particle semianalytic approach to a single Anderson impurity attached to two biased metallic leads. The theory is based on reduced parquet equations justified in critical regions of singularities in the Bethe-Salpeter equations. It offers a way to treat one-particle and two-particle thermodynamic and spectral quantities on the same footing. The two-particle vertices are appropriately renormalized so that spurious transitions into the magnetic state of the weak-coupling approximations are suppressed. The unphysical hysteresis loop in the current-voltage characteristics is thereby eliminated. Furthermore, in the linear response regime, we qualitatively reproduce the three transport regimes with the increasing temperature: from the Kondo resonant tunneling through the Coulomb-blockade regime up to a sequential tunneling regime. Far from equilibrium, we find that the bias plays a similar role as the temperature in destroying the Kondo resonant peak when the corresponding energy scale is comparable with the Kondo temperature. Aside from that, the applied voltage in low bias is shown to develop spectral peaks around the lead chemical potentials as observed in previous theoretical and experimental studies.

Laser Cooling beyond Rate Equations: Approaches from Quantum Thermodynamics

Solids can be cooled by driving impurity ions with lasers, allowing them to transfer heat from the lattice phonons to the electromagnetic surroundings. This exemplifies a quantum thermal machine, which uses a quantum system as a working medium to transfer heat between reservoirs. We review the derivation of the Bloch-Redfield equation for a quantum system coupled to a reservoir, and its extension, using counting fields, to calculate heat currents. We use the full form of this equation, which makes only the weak-coupling and Markovian approximations, to calculate the cooling power for a simple model of laser cooling. We compare its predictions with two other time-local master equations: the secular approximation to the full Bloch-Redfield equation, and the Lindblad form expected for phonon transitions in the absence of driving. We conclude that the full Bloch-Redfield equation provides accurate results for the heat current in both the weak- and strong- driving regimes, whereas the other forms have more limited applicability. Our results support the use of Bloch-Redfield equations in quantum thermal machines, despite their potential to give unphysical results.