Table of contents

We investigate the effects of localized integrability-breaking perturbations on the large times dynamics of thermodynamic one-dimensional quantum and classical systems. In particular, we suddenly activate an impurity which breaks the integrability of an otherwise homogeneous system. We focus on the large times dynamics and on the thermalization properties of the impurity, which is shown to have mere perturbative effects even at infinite times, thus preventing thermalization. This is in clear contrast with homogeneous integrability-breaking terms, which display the prethermalization paradigm and are expected to eventually cause thermalization, no matter the weakness of the integrability-breaking term. Analytic quantitative results are obtained in the case in which the bulk Hamiltonian is free and the impurity interacting.

It is shown that the time-averaged dynamics of memristors and their networks periodically driven by alternating-polarity pulses may converge to fixed-point attractors. Starting with a general memristive system model, we derive basic equations describing the fixed-point attractors and investigate attractors in the dynamics of ideal, threshold-type and second-order memristors, and memristive networks. A memristor potential function is introduced, and it is shown that in some cases the attractor identification problem can be mapped to the problem of potential function minimization. Importantly, the fixed-point attractors may only exist if the function describing the internal state dynamics depends on an internal state variable. Our findings may be used to tune the states of analog memristors, and also be relevant to memristive synapses subjected to forward- and back-propagating spikes.

We consider M clusters of interacting particles, whose in-group interactions are arbitrary, and inter-group interactions are approximated by oscillator potentials. We show that there are masses and frequencies that decouple the in-group and inter-group degrees of freedom, which reduces the initial problem to M independent problems that describe each of the relative in-group systems. The dynamics of the M center-of-mass coordinates is described by the analytically solvable problem of M coupled harmonic oscillators. This letter derives and discusses these decoupling conditions. Furthermore, to illustrate our findings, we consider a charged impurity interacting with a ring of ions. We argue that the impurity can be used to probe the center-of-mass dynamics of the ions.

Characterizing dynamical patterns in the (physical) state space of stochastic processes can be a challenging task. From two visualization techniques, the observable-representation and k-means clustering, a unified framework to identify such structures is developed. The only information required is the system transition matrix R (a quantity that can be directly accessed from experimental data). The approach is illustrated through the analysis of random searches for targets distributed in patchy environments. The protocol —for R constructed from a typical tracked long trajectory— is able to reveal the shape and locations of all the landscape patches. The method constitutes a valuable new tool to study the underlying geometry of general stochastic processes.

We describe a new concept of multimodal super-resolution imaging which combines the cumulant analysis from Super-resolution Optical Fluctuation Imaging (SOFI) with the imprinting of three-dimensional, spectral or other information into peculiar Point-Spread Function (PSF) patterns. This concept allows for encoding multidimensional or multimodal information into a single image plane and to extract this information by an appropriate spatio-temporal correlation analysis of emitter fluctuations. Here, we develop the general theory of this concept, and present proof-of-principle experiments of three-dimensional super-resolution imaging.

We investigate the norms of the Bloch vectors for any quantum state with subsystems less than or equal to four. Tight upper bounds of the norms are obtained, which can be used to derive tight upper bounds for entanglement measures defined by the norms of Bloch vectors. By using these bounds a trade-off relation of the norms of Bloch vectors is discussed. These upper bounds are then applied on separability. Necessary conditions are presented for different kinds of separable states in four-partite quantum systems. We further present a complete classification of quantum states for four-qudits quantum systems.

We show that it is possible to construct a quantum absorption refrigerator that provides refrigeration only in the transient regime, by using three interacting qubits, each of which is also interacting with a local heat bath. Though the machine does not provide any effective cooling in the steady state, significant cooling of a qubit can be achieved much before the system reaches its steady state. We also demonstrate a scenario where the temperature of the qubit that has to be cooled, decreases monotonically to its minimum steady-state temperature. This facilitates bypassing of precise time control in cooling. We study the behaviour of the ratio of the heat currents of the machine for both the scenarios. The results remain qualitatively unchanged for different models of thermal baths. We also comment on the temporal behaviour of bipartite and multipartite quantum correlations present in the system, when transient cooling without steady-state cooling takes place.

Milling is a collective circular motion often observed in nature (e.g., in fish schools) and in many theoretical models of collective motion. In these models particles are considered to be identical. However, this is not the case in nature, where even individuals of the same species differ from each other in one or more traits. In order to get insights into the mechanisms of milling formation in heterogeneous systems (i.e., with non-identical particles), the emergence of milling in a binary mixture of particles that differ in one trait is investigated for the first time. Depending on parameter values, particles that in single-type systems do not mill can either be induced to mill or destroy the milling of other particles. Milling-induction and milling-destruction are studied varying the speed, the field of view, and the relative amount of the two types of particles.

The Airy_β point process, $a_i \equiv N^{2/3} (\lambda_i-2)$, describes the eigenvalues $\lambda_i$ at the edge of the Gaussian β ensembles of random matrices for large matrix size $N \to \infty$. We study the probability distribution function (PDF) of linear statistics ${\sf L}= \sum_i t \varphi(t^{-2/3} a_i)$ for large parameter t. We show the large deviation forms ${\Bbb E}_{{\rm Airy},\,\beta}[\exp(-{\sf L})] \sim \exp(- t^2 \Sigma[\varphi])$ and $P({\sf L}) \sim \exp(- t^2 G(L/t^2))$ for the cumulant generating function and the PDF. We obtain the exact rate function, or excess energy, $\Sigma[\varphi]$ using four apparently different methods: i) the electrostatics of a Coulomb gas, ii) a random Schrödinger problem, i.e., the stochastic Airy operator, iii) a cumulant expansion, iv) a non-local non-linear differential Painlevé-type equation. Each method was independently introduced previously to obtain the lower tail of the Kardar-Parisi-Zhang equation. Here we show their equivalence in a more general framework. Our results are obtained for a class of functions φ, the monotonous soft walls, containing the monomials $\varphi(x)=(u+x)_+^\gamma$ and the exponential and equivalently describe the response of a Coulomb gas pushed at its edge. The small u behavior of the excess energy exhibits a change between a non-perturbative hard-wall–like regime for $\gamma<3/2$ (third-order free-to-pushed transition) and a perturbative deformation of the edge for $\gamma>3/2$ (higher-order transition). Applications are given, among them i) truncated linear statistics such as $\sum_{i=1}^{N_1} a_i$, leading to a formula for the PDF of the ground-state energy of $N_1 \gg 1$ non-interacting fermions in a linear plus random potential, ii) $(\beta-2)/r^2$ interacting spinless fermions in a trap at the edge of a Fermi gas, iii) traces of large powers of random matrices.

We show that observing the trajectories of confined particles in a thermal equilibrium state yields an estimate on the free-space diffusion coefficient. For generic trapping potentials and interactions between particles, the estimate comes in the form of a lower bound on the true diffusion coefficient. For non-interacting particles in parabolic trapping potentials, which approximately describes many experimental situations, the estimate is asymptotically exact. This allows to determine the diffusion coefficient from an equilibrium measurement, as opposed to a direct observation of diffusion, which necessarily starts from a non-equilibrium state. We explicitly demonstrate that the estimate remains quantitatively accurate in the presence of weak interactions and non-parabolic corrections.

Applying an external electric field on a graphene surface is an important way to improve the molecular adsorption capability of graphene, thus pull-in instability of suspended graphene sensors becomes a critical issue. Incorporating residual built-in strains, fringing fields and intermolecular forces, an electromechanical model is developed to characterize the nonlinear pull-in behaviors of suspended graphene-based sensors. The obtained results of pull-in voltages agree well with the reported experimental data. Moreover, the fracture failure of graphene sensors is initially compared to the pull-in failure. To avoid pull-in instability and fracture failure, critical formulas of axial pre-stress for zigzag-oriented and armchair-oriented graphene sensors are derived. It is demonstrated that axial pre-stress is an effective and controllable way to improve the pull-in stability of graphene sensors.

We consider the Polyakov theory of bosonic strings in conformal gauge which are used to study the conformal anomaly. However, it exhibits ghost number anomaly. We show how this anomaly can be avoided by connecting this theory to that of in background covariant harmonic gauge which is known to be free from conformal and ghost number current anomaly, by using suitably constructed finite-field-dependent BRST transformation.

Based on the principle of antenna pattern multiplication as the product of the element pattern and the array factor, a simple and flexible method to generate diffraction-limited optical hollow-tube and doughnut-spot arrays with predetermined properties is proposed. This approach can be realized in a 4Pi focusing system by reversing the field radiated from the collinear antenna array whose elements are isotropic magnetic current sources. Both hollow tubes and doughnut spots produced by this method are pure azimuthally polarized fields whose intensity distribution is nearly unchanged along the entire depth of focus. Numerical results show that the appearance and position of the focal field is determined by the element pattern and the array factor, respectively. These peculiar optical focal fields may find applications in multi-particle trapping and manipulation, materials processing, data storage, super-resolution optical microscopy and optical lithography.

An imaginary resistor (Z) based electronic dimer is used to describe the gyroscopic and resistive coupled two-level systems in quaternionic space. We successfully used the quaternionic coefficients to characterize the different classes of non-Hermitian systems: the pseudo-Hermitian and anti-Hermitian, both having exceptional points (EPs) separating the exact and the broken phases. Remarkably, the EPs conical dynamic is fully described to follow a hyperbolic/parabolic shape in the case of parity-time symmetry (PTS)/anti-PTS, respectively. Interestingly, our results demonstrated that the gyroscopic coupling mechanism allows identical non-dissipative but non-oscillatory systems with negative capacitor to exhibit PTS-like behavior.

We measure and quantify the spatial transport of energy within steady rotating hydrodynamic turbulence. A steady turbulent field in a rotating tank is perturbed by a short and abrupt increase of energy injection at a well-defined plane. Initially, a wave packet of inertial modes is generated within the background turbulent field, propagating according to the dispersion relation of inertial waves, much like wave propagation within a static fluid. At this stage, the background turbulence is only weakly affected by the pulse passage. Only at longer times, which are determined by the pulse initial amplitude and spectrum, energy is efficiently transferred from the wave packet to the background flow. The energy, which is physically injected at the bottom of the tank, is, therefore, effectively injected at a higher plane. The height of maximum energy transfer efficiency is estimated and varied via manipulations of experimental parameters.

We theoretically investigate the high-order-harmonic generation (HHG) from solids in periodic potentials. The harmonic spectrum is simulated by solving the time-dependent Schödinger equation in a monochromatic laser field. The numerical results show that the intensity of the high-order harmonics from the superposition of the conduction band minimum (CBM) and valence band maximum (VBM) states is about three orders of magnitude higher than that from the VBM alone in the plateau region. Our results show that conduction band population in the initial state affects the intensity of HHG. The physical mechanism is discussed by the picture of time-dependent population imaging (TDPI).

Nonequilibrium states of closed quantum many-body systems defy a thermodynamic description. As a consequence, constraints such as the principle of equal a priori probabilities in the microcanonical ensemble can be relaxed, which can lead to quantum states with novel properties of genuine nonequilibrium nature. In turn, for the theoretical description it is in general not sufficient to understand nonequilibrium dynamics on the basis of the properties of the involved Hamiltonians. Instead it becomes important to characterize time-evolution operators, which adds time as an additional scale to the problem. In this perspective article we summarize recent progress in the field of dynamical quantum phase transitions, which are phase transitions in time with temporal nonanalyticities in matrix elements of the time-evolution operator. These transitions are not driven by an external control parameter, but rather occur due to sharp internal changes generated solely by unitary real-time dynamics. We discuss the obtained insights on general properties of dynamical quantum phase transitions, their physical interpretation, potential future research directions, as well as recent experimental observations.

The collective behavior of synthetic micro- and nano-scale motors powered by catalytic reactions has been an active research area for understanding the fundamental principles in active matter as well as their prominent applications. In many situations, small motors should operate in out-of-equilibrium complex chemically reacting media. By making use of particle-based simulations, we study the collective dynamics of chemically powered sphere-dimer motors in a chemically oscillating medium which can supply fuels to the motors and remove the products they produce. In collections of such motors, the interactions among individual motors that arise from concentration gradients and hydrodynamic coupling, are greatly influenced by the properties of the oscillation. It is shown how oscillations of the concentrations in chemical species in the environment give rise to a periodic dispersion-aggregation transition of motor clusters. The susceptibility of the transition to the oscillation is found to be changed by the manner of fuel supplies, from the time-delay response in a harmonic oscillating medium to the synchronous response in a bistable medium. The dynamical process of clusters formation, which exhibits different regimes involving propulsive and diffusive behaviors, as well as the structure of transiently formed clusters, is analyzed. The dependence of dispersion-aggregation transition on the dimer density and the frequency of periodic oscillation is presented in a phase diagram. The results presented here will contribute to the applications when an ensemble of dimers performs their tasks in complex chemical media.

The interlayer friction force $(F_{\mathrm{f}})$ of incommensurate graphite is a key material parameter to understand the mechanism of superlubricity and the unexpected properties of carbon-based materials; however, its determination by direct experiments under different ambient temperatures and sliding velocities is yet to be reported. In this letter, we report the direct, accurate experimental measurement of the $F_{\mathrm{f}}$ of microscale incommensurate graphite. The measured $F_{\mathrm{f}}$ per unit area, $F_{\mathrm{f}}=0.015\pm 0.008\ \text{MPa}$ in ambient laboratory conditions, decreases with increasing temperature $(22~^{\circ}\text{C}\le T \le 185~^{\circ}\text{C})$, exhibits a logarithmic increase with respect to sliding velocities $(40\ \text{nm/s}\le v \le 12000\ \text{nm/s})$ and remains almost unchanged under various twist angles. At elevated temperatures, $F_{\mathrm{f}}$ can be lower than the resolution of the force sensor, which corresponds to $F_{\mathrm{f}}=0.32\ \text{kPa}$ per unit area. This is the lowest value reported for lamellar materials. These experimental measurements assist in understanding the mechanism of microscale superlubricity and such an ultra-low friction force will also introduce a wide range of applications in microelectromechanical systems (MEMS).

Determinant quantum Monte Carlo (QMC) simulations of fermion models normally face the sign problem, which has a strong dependence of the interaction strength, electron filling, temperature, lattice geometry and lattice size. It is useful to set up the data set of such dependence, to make it clear which parameter region is accessible or not. To supplement the previous study, here we report the behavior of the average sign in the weak interaction region, as functions of lattice geometry, lattice size, electron filling and temperature. Furthermore, we find that in the weak interaction region, for several interesting lattice geometries (except for the kagome lattice) the average sign gets improved when the lattice sizes increase, which is in contrast to the general understanding of the lattice size dependence of the average sign. This finding points out that when the sign problem is present in the weak interaction region, the simulation of a larger lattice size can be better under control.

We compute the Drude weight and the critical exponents as functions of the density in non-integrable generalizations of XXZ or Hubbard chains, in the critical high- or low-density regime where the dispersion becomes almost quadratic, the Luttinger liquid description breaks down and the Bethe ansatz cannot be used. Even in the regions where irrelevant terms dominate, no difference between integrable and non-integrable models appears in exponents and conductivity at zero temperature. Our results are based on a fully rigorous two-regime multiscale analysis and a recently introduced partially solvable model.

The reason why the effective-mass approximation, derived using wave functions of infinite periodic systems, works so well with nanoscopic structures, has been an enigma and a challenge for theorists. To explain this issue, we first show that the essential "only-one-band" and "band-edge" assumptions that are behind the standard derivation of the effective mass approximation are better justified for nano-structures. We show then that the effective-mass approximation can also be derived using, instead of Bloch-type wave functions, the eigenfunctions and eigenvalues obtained in the theory of finite periodic systems, where the finiteness of the number of primitive cells in nanoscopic layers is a prerequisite and a crucial condition. We also show, with specific calculations of the optical response, that the rapidly varying eigenfunctions $\Phi_{\epsilon_0,\eta_0}(z)$ of the one-band wave functions $\Psi^{\epsilon_0,\eta_0}_{\mu,\nu}(z)= {\it \Psi}^{\epsilon_0}_{\mu,\nu}(z) \Phi_{\epsilon_0,\eta_0}(z)$, can be safely dropped out for the calculation of inter-band transition matrix elements.

The interplay between external field and fluid-mediated interactions in active suspensions leads to patterns of collective motion that are poorly understood. Here, we study the hydrodynamic stability and transport of microswimmers with weak magnetic dipole moments in an external field using a kinetic theory framework. Combining linear stability analysis and non-linear 3D continuum simulations, we show that for sufficiently high activity and moderate magnetic field strengths, a homogeneous polar steady state is unstable and distinct types of splay and bend instabilities for puller and pusher swimmers emerge. The instabilities arise from the amplification of anisotropic hydrodynamic interactions due to the external alignment and lead to a partial depolarisation and a reduction of the average transport speed of the swimmers in the field direction. Interestingly, at higher field strengths the homogeneous polar state becomes stable and a transport efficiency identical to that of active particles without hydrodynamic interactions is restored.

Original article: EPL, 124 (2018) 54002.