Adiabatic Limit Research Articles

Nonequilibrium Josephson diode effect in periodically driven SNS junctions

In typical Josephson junctions, the Josephson current is an odd function of the superconducting phase difference. Recently, diode effect in Josephson junctions is observed in experiments wherein the maximum and the minimum values of the Josephson current in the current-phase relation do not have the same magnitude. We propose a superconductor-normal metal-superconductor (SNS) junction where Josephson diode effect manifests when the normal metal region is driven. Time reversal symmetry and inversion symmetry need to be broken in the SNS junction for the diode effect to show up. We calculate long time averaged current and show that the system exhibits diode effect for two configurations of the driven SNS junction - one in which inversion symmetry is broken in the undriven part of the Hamiltonian and the other wherein both the symmetries are broken by the driving potential. In the latter configuration, a nonzero current known as anomalous current appears at the junction in absence of phase bias. In the proposed setup, the diode effect vanishes in the adiabatic limit.

Ratchet universality in the directed motion of spheres by unbiased driving forces in viscous fluids

Directed motion of a sphere immersed in a viscous fluid and subjected solely to a nonlinear drag force and zero-average biharmonic forces is studied in the absence of any periodic substrate potential. We consider the case of two mutually perpendicular sinusoidal forces of periods T and T/2, respectively, which cannot yield any ratchet effect when acting separately, while inducing directed motion by acting simultaneously. Remarkably and unexpectedly, the dependence on the relative amplitude of the two sinusoidal forces of the average terminal velocity is theoretically explained from the theory of ratchet universality, while extensive numerical simulations confirmed its predictions in the adiabatic limit. Additionally, the dependence on the dimensionless driving frequency of the dimensionless average terminal velocity far from the adiabatic limit is qualitatively explained with the aid of the vibrational mechanics approach.

Concentration of mass in the vanishing adiabatic exponent limit of Aw–Rascle traffic model with relaxation

Concentration of mass in the vanishing adiabatic exponent limit of Aw–Rascle traffic model with relaxation

An insulated column for lab-scale non-isothermal breakthrough: Impact of thermal effects during CO2 adsorption

Often lab-scale adsorptive breakthrough experiments are conducted in an isothermal manner, whereas industrial-scale adsorption processes are near-adiabatic. In this work, a polyurethane (PUR) insulating column was manufactured to mimic large-scale non-isothermal behavior via laboratory-scale breakthrough tests. Breakthrough tests with a CO2/N2 gas mixture on zeolite 13X (∼5 g) were performed. A bed temperature increase of 62 °C and long cooling times were observed. When compared to a regular steel column, showing a temperature rise of only 12 °C, the column efficiency was approximately 20% lower due to adiabatic effects. The heat evacuated from the adsorbent bed via the column exhaust was used as a measure for the degree of adiabaticity. Up to 46% of the theoretical heat of adsorption could be detected at the PUR column exhaust compared to 4% at the steel column exhaust. The important difference between isothermal, non-isothermal and adiabatic limit behavior was demonstrated through breakthrough experiments and simulations.

On the applicability of the Landau-Zener formula to axion-photon conversion

Axions and photons resonantly interconvert in regions where the plasma frequency approximately equals the axion mass. This process is directly analogous to an avoided level crossing in quantum mechanics, for which the celebrated Landau-Zener (LZ) formula provides a simple, non-perturbative solution for the conversion probability. The LZ formula is commonly used in studies of axion-photon conversion; however, in this context, it relies on the assumption that the magnetic field variation is small compared to variations of the plasma frequency, which is frequently not the case in real plasmas.We derive a generalised version of the LZ formula by allowing the boundaries to be located at a scale that is similar to the inhomogeneities. We find that the LZ formula fails when the oscillation range is small compared to the resonance region. This failure is more severe in the adiabatic limit, when the plasma frequency varies slowly, resulting ina conversion probability that is not maximal as opposed to a naive application of the LZ formula.Moreover, we consider circumstances where the generalised LZ formula does not apply and present an alternative semi-classical approximation with complementary regime of validity.

Out-of-equilibrium finite-size scaling in generalized Kibble-Zurek protocols crossing quantum phase transitions in the presence of symmetry-breaking perturbations

We study the effects of symmetry-breaking perturbations in the out-of-equilibrium quantum dynamics of many-body systems slowly driven by a time-dependent symmetry-preserving parameter, across the quantum critical regime associated with a continuous quantum transition (CQT). For this purpose, we analyze the out-of-equilibrium dynamics arising from generalized Kibble-Zurek (KZ) protocols, within a dynamic renormalization-group framework allowing for finite-size systems. We show that the time dependence of generic observables develops an out-of-equilibrium finite-size scaling (FSS) behavior, arising from the interplay between the timescale ${t}_{s}$ of the parameter variations in the KZ protocol, the size $L$ of the system, and the strength $h$ of the symmetry-breaking perturbation, in the limit of large ${t}_{s}$ and $L$. Moreover, scaling arguments based on the first-order adiabatic approximation of slow variations in quantum systems allow us to characterize the approach to the adiabatic regimes for some limits of the model parameters (for example, when we take ${t}_{s}\ensuremath{\rightarrow}\ensuremath{\infty}$ before $L\ensuremath{\rightarrow}\ensuremath{\infty}$), predicting asymptotic power-law suppressions of the nonadiabatic behaviors in the adiabatic limits. This out-of-equilibrium FSS is supported by numerical analyses for the paradigmatic quantum Ising chain along generalized KZ protocols, with a time-dependent transverse field crossing its CQT, in the presence of a static longitudinal field breaking the ${\mathbb{Z}}_{2}$ symmetry.

Equilibrium states for the massive Sine-Gordon theory in the Lorentzian signature

In this paper we investigate the massive Sine-Gordon model in the ultraviolet finite regime in thermal states over the two-dimensional Minkowski spacetime. We combine recently developed methods of perturbative algebraic quantum field theory with techniques developed in the realm of constructive quantum field theory over Euclidean spacetimes to construct the correlation functions of the equilibrium state of the Sine-Gordon theory in the adiabatic limit. First of all, the observables of the Sine-Gordon theory are seen as functionals over the free configurations and are obtained as a suitable combination of the S−matrices of the interaction Lagrangian restricted to compact spacetime regions over the free massive theory. These S−matrices are given as power series in the coupling constant with values in the algebra of fields over the free massive theory. Adapting techniques like conditioning and inverse conditioning to spacetimes with Lorentzian signature, we prove that these power series converge when evaluated on a generic field configuration. The latter observation implies convergence in the strong operator topology in the GNS representations of the considered states. In the second part of the paper, adapting the cluster expansion technique to the Lorentzian case, we prove that the correlation functions of the interacting equilibrium state at finite temperature (KMS state) can be constructed also in the adiabatic limit, where the interaction Lagrangian is supported everywhere in space.

Rayleigh-Taylor instability in an adiabatic-radiative rare plasma

Considering the particle nature of photons, the impact of electromagnetic radiation pressure is examined on the Rayleigh-Taylor instability (RTI) in a non-uniform rare magnetoplasma. For low-density and high-temperature rare plasma, the RTI with radiation pressure is revisited in the adiabatic limit. The growth rate conditions and propagating modes are derived using the framework of a developed fluid model. For specific values of ion temperature, the cut-off values of propagation of the fringing instability is found to be temperature dependent. A numerical comparison of the present results with previous work Maryam N, Rozina C and Ali S (2021, IEEE Transactions on Plasma Science 49 1072–1078) is displayed in table 1. It is found that the radiative acoustic speed is increased due to electromagnetic radiation pressure in rare plasmas as compared to radiative acoustic speed in dense plasmas. However, the growth rate of RTI increases comparatively as function of radiation pressure in rare plasmas. The present findings reveals that the consequences of RTI are remarkably concerned with the choice of electromagnetic radiation pressure either in dense (astrophysical) or rare (laboratory) plasmas. These findings are relevant to the observations of long-lived irregularities for explaining the gravitational instability in laboratory plasmas, e.g. in fusion devices like tokamaks.

A Note on Adiabatic Time Evolution and Quasi-Static Processes in Translation-Invariant Quantum Systems

We study the slowly varying, non-autonomous quantum dynamics of a translation-invariant spin or fermion system on the lattice $$\mathbb {Z}^d$$ . This system is assumed to be initially in thermal equilibrium, and we consider realizations of quasi-static processes in the adiabatic limit. By combining the Gibbs variational principle with the notion of quantum weak Gibbs states introduced in Jakšić et al. (Approach to equilibrium in translation-invariant quantum systems: some structural results, in the present issue of Ann. H. Poincaré, 2023), we establish a number of general structural results regarding such realizations. In particular, we show that such a quasi-static process is incompatible with the property of approach to equilibrium studied in this previous work.

Accretion within the innermost stable circular orbit: analytical thermodynamic solutions in the adiabatic limit

ABSTRACT We present analytical solutions for the thermodynamic (temperature, pressure, density, etc.) properties of thin accretion flows in the region within the innermost stable circular orbit (ISCO) of a Kerr black hole, the first analytical solutions of their kind. These solutions are constructed in the adiabatic limit and neglect radiative losses, an idealization valid for a restricted region of parameter space. We highlight a number of remarkable properties of these solutions, including that these solutions cool for radii rI/2 < r < rI, before increasing in temperature for 0 < r < rI/2, independent of black hole spin and assumptions regarding the equation of state of the accretion flow. The radiative temperature of these solutions can, for some values of the free parameters of the theory, peak within the ISCO and not in the main body of the disc. These solutions represent a fundamentally new class of analytical accretion solutions, which are both non-circular and non-radial in character.

Correspondence between Dicke-model semiclasscial dynamics in the superradiant dipolar phase and the Euler heavy top

Analytic expression is found for the frequency dependence of the transmission coefficient of a transmission line inductively coupled to the microwave cavity with the superradiant condensate. Sharp transmission drops reflect the condensate's frequencies spectrum. These results pave the way to direct detection of emergence of the superradiant condensates in quantum metamaterials. Results are based on the analytic solutions of the nonlinear semiclassical dynamics of the superradiant photonic condensate in the Dicke model of an ensemble of two-level atoms dipolar coupled to the electromagnetic field in the microwave cavity. In the adiabatic limit with respect to the photon degree of freedom, the system is approximately integrable with evolution being expressed via Jacobi elliptic functions of real time. Depending on the coupling strength, the semiclassical coordinate of the superradiant condensate in the ground state either oscillates in one of the two degenerate minima of the condensate's potential energy or traverses between them over the saddle point. An experimental setup for measuring of the breakdown of the normal phase of the Dicke model via coupling to the transmission line is proposed. A one-to-one mapping of the semiclassical motion of the superradiant condensate on the nodding of unstable Lagrange ``sleeping top'' also turns the Dicke model into an analog device for modeling the dynamics of mechanical systems.

Topologically protected quantum dynamo effect in a driven spin-boson model

We describe a quantum dynamo effect in a driven system coupled to a harmonic oscillator describing a cavity mode or to a collection of modes forming an Ohmic bosonic bath. When the system Hamiltonian changes in time, this induces a dynamical field in the bosonic modes having resonant frequencies with the driving velocity. This field opposes the change of the external driving field in a way reminiscent of Faraday's law of induction, justifying the term 'quantum dynamo effect'. For the specific situation of a periodically driven spin-$\frac{1}{2}$ on the Bloch sphere, we show that the work done by rolling the spin from north to south pole can efficiently be converted into a coherent displacement of the resonant bosonic modes, the effect thus corresponds to a work-to-work conversion and allows to interpret this transmitted energy into the bath as work. We study this effect, its performance and limitations in detail for a driven spin-$\frac{1}{2}$ in the presence of a radial magnetic field addressing a relation with topological systems through the formation of an effective charge in the core of the sphere. We show that the dynamo effect is directly related to the dynamically measured topology of this spin-$\frac{1}{2}$ and thus in the adiabatic limit provides a topologically protected method to convert driving work into a coherent field in the reservoir. The quantum dynamo model is realizable in mesoscopic and atomic systems.

Time-based Chern number in periodically driven systems in the adiabatic limit

To define the topology of driven systems, recent works have proposed synthetic dimensions as a way to uncover the underlying parameter space of topological invariants. Using time as a synthetic dimension, together with a momentum dimension, gives access to a synthetic two-dimensional ($2\mathrm{D}$) Chern number. It is, however, still unclear how the synthetic 2D Chern number is related to the Chern number that is defined from a parametric variable that evolves with time. Here we show that in periodically driven systems in the adiabatic limit, the synthetic $2\mathrm{D}$ Chern number is a multiple of the Chern number defined from the parametric variable. The synthetic 2D Chern number can thus be engineered via how the parametric variable evolves in its own space. We justify our claims by investigating Thouless pumping in two one-dimensional ($1\mathrm{D}$) tight-binding models, a three-site chain model, and a two-$1\mathrm{D}$-sliding-chains model. The present findings could be extended to higher dimensions and other periodically driven configurations.

Non-Gaussian work statistics at finite-time driving

We study properties of the work distribution of a many-body system driven through a quantum phase transition in finite time. We focus on the non-Gaussianity of the distribution, which we characterize through two quantitative metrics: skewness and negentropy. In particular, we focus on the quantum Ising model and show that a finite duration of the ramp enhances the non-Gaussianity of the distribution for a finite size system. By examining the characteristics of the full distribution, we observe that there is a clear intermediate regime between the sudden quench and adiabatic limits, where the distribution becomes increasingly skewed.

Torsional birefringence in metric-affine Chern-Simons gravity: gravitational waves in late-time cosmology

In the context of the metric-affine Chern-Simons gravity endowed with projective invariance, we derive analytical solutions for torsion and nonmetricity in the homogeneous and isotropic cosmological case, described by a flat Friedmann-Robertson-Walker metric. We discuss in some details the general properties of the cosmological solutions in the presence of a perfect fluid, such as the dynamical stability and the emergence of big bounce points, and we examine the structure of some specific solutions reproducing de Sitter and power law behaviours for the scale factor. Then, we focus on first-order perturbations in the de Sitter scenario, and we study the propagation of gravitational waves in the adiabatic limit, looking at tensor and scalar polarizations. In particular, we find that metric tensor modes couple to torsion tensor components, leading to the appearance, as in the metric version of Chern-Simons gravity, of birefringence, characterized by different dispersion relations for the left and right circularized polarization states. As a result, the purely tensor part of torsion propagates like a wave, while nonmetricity decouples and behaves like a harmonic oscillator. Finally, we discuss scalar modes, outlining as they decay exponentially in time and do not propagate.

Adiabatic limit collapse and local interaction effects in non-linear active microrheology molecular simulations of two-dimensional fluids.

Nonlinear active microrheology molecular dynamics simulations of high-density two-dimensional fluids show that the presence of strong confining forces and an external pulling force induces a correlation between the velocity and position dynamics of the tracer particle. This correlation manifests in the form of an effective temperature and an effective mobility of the tracer particle, which is responsible for the breaking of the equilibrium fluctuation-dissipation theorem. This fact is shown by measuring the tracer particle's temperature and mobility directly from the first two moments of the velocity distribution of a tracer particle and by formulating a diffusion theory in which effective thermal and transport properties are decoupled from the velocity dynamics. Furthermore, the flexibility of the attractive and repulsive forces in the tested interaction potentials allowed us to relate the temperature and mobility behaviors to the nature of the interactions and the structure of the surrounding fluid as a function of the pulling force. These results provide a refreshing physical interpretation of the phenomena observed in non-linear active microrheology.

Onset of triple-diffusive convective stability in the presence of a heat source and temperature gradients: An exact method

<abstract> <p>In the current work, in the presence of a heat source and temperature gradients, the onset of triple-diffusive convective stability is studied for a fluid, and a fluid-saturated porous layer confined vertically by adiabatic limits for the Darcy model is thoroughly analyzed. With consistent heat sources in both layers, this composite layer is subjected to three temperature profiles with Marangoni effects. The fluid-saturated porous region's lower boundary is a rigid surface, while the fluid region's upper boundary is a free surface. For the system of ordinary differential equations, the thermal surface-tension-driven (Marangoni) number, which also happens to be the Eigenvalue, is solved in closed form. The three different temperature profiles are investigated, the thermal surface-tension-driven (Marangoni) numbers are calculated analytically, and the effects of the heat source/sink are studied in terms of corrected internal Rayleigh numbers. Graphs are used to show how different parameters have an impact on the onset of triple-diffusive convection. The study's parameters have a greater influence on porous layer dominant composite layer systems than on fluid layer dominant composite layer systems. Finally, porous parameters and corrected internal Rayleigh numbers are stabilize the system, and solute1 Marangoni number and ratio of solute2 diffusivity to thermal diffusivity of fluid are destabilize the system.</p> </abstract>

Dynamical Pair Production at Sub-Barrier Energies for Light Nuclei

In the collision of two heavy ions, the strong repulsion coming from the Coulomb field is enough to produce e+e− pair(s) from vacuum fluctuations. The energy is provided by the kinetic energy of the ions and the Coulomb interaction at the production point. If, for instance, the electron is located at the center of mass (C.M.) of the two ions moving along the z-axis, and the positron is at a distance x from the electron, the ions can be accelerated towards each other since the Coulomb barrier is lowered by the presence of the electron. This screening results in an increase in the kinetic energy of the colliding ions and may result in an increase in the fusion probability of light ions above the adiabatic limit.

Adiabaticity in nonreciprocal Landau-Zener tunneling

We investigate the Landau-Zener tunneling (LZT) of a self-interacting two-level system in which the coupling between the levels is nonreciprocal. In such a non-Hermitian system, when the energy bias between two levels is adjusted very slowly, i.e., in the adiabatic limit, we find that a quantum state can still closely follow the eigenstate solution until it encounters the exceptional points (EPs) at which two eigenvalues and their corresponding eigenvectors coalesce. In the absence of the nonlinear self-interaction, we can obtain explicit expressions for the eigenvectors and eigenvalues and analytically derive the adiabatic LZT probability from invariants at EPs. In the presence of the nonlinear interaction, the dynamics of the adiabatic evolutions are explicitly demonstrated with the help of classical trajectories in the plane of the two canonical variables of the corresponding classical Josephson Hamiltonian. We show that the adiabatic tunneling probabilities can be precisely predicted by the classical action at EPs in the weak nonreciprocal regime. In a certain region of strong nonreciprocity, we find that interestingly, the nonlinear interaction effects can be completely suppressed so that the adiabatic tunneling probabilities are identical to their linear counterparts. We also obtain a phase diagram for large ranges of nonreciprocity and nonlinear interaction parameters to explicitly demonstrate where the adiabaticity can break down, i.e., the emergence of the nonzero tunneling probabilities even in adiabatic limit.

Probing quantum many-body correlations by universal ramping dynamics

Ramping a physical parameter is one of the most common experimental protocols in studying a quantum system, and ramping dynamics has been widely used in preparing a quantum state and probing physical properties. Here, we present a novel method of probing quantum many-body correlation by ramping dynamics. We ramp a Hamiltonian parameter to the same target value from different initial values and with different velocities, and we show that the first-order correction on the finite ramping velocity is universal and path-independent, revealing a novel quantum many-body correlation function of the equilibrium phases at the target values. We term this method as the non-adiabatic linear response since this is the leading order correction beyond the adiabatic limit. We demonstrate this method experimentally by studying the Bose-Hubbard model with ultracold atoms in three-dimensional optical lattices. Unlike the conventional linear response that reveals whether the quasi-particle dispersion of a quantum phase is gapped or gapless, this probe is more sensitive to whether the quasi-particle lifetime is long enough such that the quantum phase possesses a well-defined quasi-particle description. In the Bose-Hubbard model, this non-adiabatic linear response is significant in the quantum critical regime where well-defined quasi-particles are absent. And in contrast, this response is vanishingly small in both superfluid and Mott insulators which possess well-defined quasi-particles. Because our proposal uses the most common experimental protocol, we envision that our method can find broad applications in probing various quantum systems.