We obtain an exact analytic expression for the average distribution, in the thermodynamic limit, of overlaps between two copies of the same random energy model (REM) at different temperatures. We quantify the non-self averaging effects and provide an exact approach to the computation of the fluctuations in the distribution of overlaps in the thermodynamic limit. We show that the overlap probabilities

By characterizing the time evolution of COVID-19 in term of its ‘velocity’ (log of the new cases per day) and its rate of variation, or ‘acceleration’, we show that in many countries there has been a deceleration even before lockdowns were issued. This feature, possibly due to the increase of social awareness, can be rationalized by a susceptible-hidden-infected-recovered model introduced by Barnes

We demonstrate that a large class of first-order quantum phase transitions, namely, transitions in which the ground state energy per particle is continuous but its first order derivative has a jump discontinuity, can be described as a condensation in the space of states. Given a system having Hamiltonian H = K + gV , where K and V are two non commuting operators acting on the space of states ##IMG##

We consider the area functional defined by the integral of an Ornstein–Uhlenbeck process which starts from a given value and ends at the time it first reaches zero (its equilibrium level). Exact results are presented for the mean, variance, skewness and kurtosis of the underlying area probability distribution, together with the covariance and correlation between the area and the first passage time

Any kind of quantum resource useful in different information processing tasks is vulnerable to several types of environmental noise. Here we study the behaviour of quantum correlations such as entanglement and steering in two-qubit systems under the application of the generalised amplitude damping channel and propose two protocols towards preserving them under this type of noise. First, we employ the

We propose the systematic construction of classical and quantum two-dimensional space-time lattices primarily based on algebraic considerations, i.e. on the existence of associated r -matrices and underlying spatial and temporal classical and quantum algebras. This is a novel construction that leads to the derivation of fully discrete integrable systems governed by sets of consistent integrable non-linear

A free boson on a lattice is the simplest field theory one can think of. Its partition function can be easily computed in momentum space. However, this straightforward solution hides its integrability properties. Here, we use the methods of exactly solvable models, that are currently applied to spin systems, to a massless and massive free boson on a 2D lattice. The Boltzmann weights of the model are

Random aggregates of hard spheres can be formed either by aggregation or by dynamic reorganization. The resulting two broad families of aggregates present different geometrical structures that have not been studied in a systematic fashion to this day. We investigate various structural indicators (contact coordination number, Delaunay tetrahedra, Voronoi polyhedra, pair distribution functions,…) of

Considering a general diffusion process that runs over the non-negative half-line, this paper addresses the first-passage time (FPT) to the origin: the time it takes the process to get from an arbitrary fixed positive level to the level zero. Inspired by the special features of Brownian motion, three types of FPT selfsimilarity are introduced: (i) stochastic, which holds in ‘real space’; (ii) Laplace

The Weyl–Wigner representations for canonical thermal equilibrium quantum states are obtained for the whole class of quadratic Hamiltonians through a Wick rotation of the Weyl–Wigner symbols of Heisenberg and metaplectic operators. The behavior of classical structures inherently associated to these unitaries is described under the Wick mapping, unveiling that a thermal equilibrium state is fully determined

We introduce procedures for decomposing N × N unitary matrices into smaller M × M unitary matrices. Our procedures enable designing modular and optimal architectures for implementing arbitrary discrete unitary transformations on light. Such architectures rely on systematically combining the M -mode linear optical interferometers together to implement a given N -mode transformation. Thus this work enables

In this paper, we propose and study integrable discrete systems related to the classical Boussinesq system. Based on elementary and binary Darboux transformations and associated Bäcklund transformations, both full-discrete systems and semi-discrete systems are constructed. The discrete systems obtained from elementary Darboux transformation are shown to be the discrete systems of relativistic Toda

We study numerically the ODE/IM correspondence for untwisted affine Lie algebras associated with simple Lie algebras including exceptional type. We consider the linear problem obtained from the massless limit of that of the modified affine Toda field equation. We found that the Q -functions in integrable models are expressed as the inner product of the solution of the dual linear problem and the subdominant

It is shown that asymptotically consistent modifications of (Boussinesq-like) shallow water approximations, in order to improve their dispersive properties, can fail for uneven bottoms (i.e., the dispersion is actually not improved). It is also shown that these modifications can lead to ill-posed equations when the water depth is not constant. These drawbacks are illustrated with the (fully nonlinear

We study the extremal properties of a stochastic process x t defined by a Langevin equation ##IMG## [http://ej.iop.org/images/1751-8121/54/4/04LT01/aabd42cieqn1.gif] {${\dot {x}}_{t}=\sqrt{2{D}_{0}V\left({B}_{t}\right)}\enspace {\xi }_{t}$} , where ξ t is a Gaussian white noise with zero mean, D 0 is a constant scale factor, and V ( B t ) is a stochastic ‘diffusivity’ (noise strength), which itself

We consider a class of trigonometric solutions of Witten–Dijkgraaf–Verlinde–Verlinde equations determined by collections of vectors with multiplicities. We show that such solutions can be restricted to special subspaces to produce new solutions of the same type. We find new solutions given by restrictions of root systems, as well as examples which are not of this form. Further, we consider a closely

A heterostructure composed of two parallel homogeneous layers is studied in the limit as their widths l 1 and l 2 , and the distance between them r shrinks to zero simultaneously. The problem is investigated in one dimension and the squeezing potential in the Schrödinger equation is given by the strengths V 1 and V 2 depending on the layer thickness. A whole class of functions V 1 ( l 1 ) and V 2 (

We study the epidemic spreading on spatial networks where the probability that two nodes are connected decays with their distance as a power law. As the exponent of the distance dependence grows, model networks smoothly transition from the random network limit to the regular lattice limit. We show that despite keeping the average number of contacts constant, the increasing exponent hampers the epidemic

In this article we investigate driven dissipative quantum dynamics of an ensemble of two-level systems given by a Markovian master equation with collective and local dissipators. Exploiting the permutation symmetry in our model, we employ a phase space approach for the solution of this equation in terms of a diagonal representation with respect to certain generalized spin coherent states. Remarkably

We propose a simple Langevin equation as a generator for a noise process with Laplace-distributed values (pure exponential decays for both positive and negative values of the noise). We calculate explicit expressions for the correlation function, the noise intensity, and the correlation time of this noise process and formulate a scaled version of the generating Langevin equation such that correlation

In two-party, two-input and two-output measurement scenario only relevant Bell’s inequality is the Clauser–Horne–Shimony–Holt (CHSH) form. They also provide the necessary and sufficient conditions (NSCs) for local realism. Any other form, such as, Clauser–Horne and Wigner forms reduce to the CHSH one. The standard Leggett–Garg inequalities, proposed for testing incompatibility between macrorealism

We establish a convex resource theory of non-Markovianity inducing information backflow under the constraint of small time intervals within the temporal evolution. We identify the free operations and a generalized bona-fide measure of non-Markovian information backflow. The framework satisfies the basic properties of a consistent resource theory. The proposed resource quantifier is lower bounded by

We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width, which goes beyond the usual techniques applied to quasi-exactly solvable models. We map the time-independent Schrödinger equation onto the Heun confluent differential equation, which is solved by using an infinite power series. The coefficients

In this work the momentum spreading of a multidimensional hydrogenic system in highly excited (Rydberg) states is quantified by means of the Rényi and Shannon entropies of its momentum probability density. These quantities, which rest at the core of numerous fields from atomic and molecular physics to quantum technologies, are determined by means of a methodology based on the strong degree-asymptotics

We construct SU(2|1), d = 1 supersymmetric models based on the coupling of dynamical and semi-dynamical (spin) multiplets, where the interaction term of both multiplets is defined on the generalized chiral superspace. The dynamical multiplet is defined as a chiral multiplet ( 2 , 4 , 2 ), while the semi-dynamical multiplet is associated with a multiplet ( 4 , 4 , 0 ) of the mirror type.

We present an analytic proof of the existence of phase transition in the large N limit of certain random noncommutative geometries. These geometries can be expressed as ensembles of Dirac operators. When they reduce to single matrix ensembles, one can apply the Coulomb gas method to find the empirical spectral distribution. We elaborate on the nature of the large N spectral distribution of the Dirac

Godrèche, in Comment on ‘Fluctuation dominated phase ordering at a mixed order transition’ [ J. Phys. A: Math. Theor. the J. Phys. A reference to the Comment by C. Godreche], has commented on our recent paper Fluctuation dominated phase ordering at a mixed order transition (2019 J. Phys. A: Math. Theor. 52 254001). This comment concerns the prefactor of the cusp-like small-argument singularity of the

When the contacts of an open system flip between different reservoirs, the resulting nonequilibrium shows increased dynamical activity. We investigate such active gating for one-dimensional symmetric (SEP) and asymmetric (ASEP) exclusion models where the left/right boundary rates for entrance and exit of particles are exchanged at random times. Such rocking makes simple exclusion processes spatially

We critically discuss the problem of finding the λ -index ##IMG## [http://ej.iop.org/images/1751-8121/54/2/025002/aabccf9ieqn2.gif] {$\mathcal{N}\left(\lambda \right)\in \left[0,1,\dots ,N\right]$} of a real symmetric matrix M , defined as the number of eigenvalues smaller than λ , using the entries of M as only input. We show that a widely used formula ##IMG## [http://ej.iop.org/images/1751-8121/

We study the non-equilibrium steady states in a closed system consisting of interacting particles obeying exclusion principle with quenched hopping rate. Cluster mean field approach is utilized to theoretically analyze the system dynamics in terms of phase diagram, density profiles, current, etc, with respect to interaction energy E . It turns out that on increasing the interaction energy beyond a

The determination of genuine entanglement is a central problem in quantum information processing. We investigate the tripartite state as the tensor product of two bipartite entangled states by merging two systems. We show that the tripartite state is a genuinely entangled (GE) state when the range of both bipartite states are entanglement-breaking (EB) subspaces. We further investigate the tripartite

The iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method for calculating analytic approximants to solutions of nonlinear ordinary differential equations with sources is elaborated upon. Diverse problems in physics are studied and approximate analytic solutions are found. We first treat a damped driven nonlinear oscillator and show that the method can correctly

We present an analytic study of conformal field theories on the real projective space ##IMG## [http://ej.iop.org/images/1751-8121/54/2/024003/aabcf59ieqn7.gif] {$\mathbb{R}{\mathbb{P}}^{d}$} , focusing on the two-point functions of scalar operators. Due to the partially broken conformal symmetry, these are non-trivial functions of a conformal cross ratio and are constrained to obey a crossing equation

The fermionization regime and entanglement correlations of two distinguishable harmonically confined fermions interacting via a zero-range potential is addressed. We present two alternative representations of the ground state that we associate with two different types of one-dimensional spaces. These spaces, in turn, induce different correlations between particles and thus require a suitable definition

We revisit the problem of determining conditions under which a pure state, that evolves under an arbitrary unitary transformation, reaches an orthogonal state in a finite amount of the transformation parameter. Simple geometric considerations disclose the existence of a fundamental limit for the minimal amount required, providing, in particular, an intuitive hint of the Mandelstam–Tamm bound. The geometric

We find the asymptotic behaviors of Toeplitz determinants with symbols which are a sum of two contributions: one analytical and non-zero function in an annulus around the unit circle, and the other proportional to a Dirac delta function. The formulas are found by using the Wiener–Hopf procedure. The determinants of this type are found in computing the spin-correlation functions in low-lying excited

In the past few years, stochastic resetting has become a subject of immense interest. Most of the theoretical studies so far focused on instantaneous resetting which is, however, a major impediment to practical realisation or experimental verification in the field. This is because in the real world, taking a particle from one place to another requires finite time and thus a generalization of the existing

The dynamics of a driven tracer in a quiescent bath subject to geometric confinement models a broad range of phenomena. We explore this dynamics in a 1D lattice model, where geometric confinement is tuned by varying the rate of particle overtaking. Previous studies of the model’s stationary properties on a ring of L sites have revealed a phase in which the bath density profile extends over an ##IMG##

In this study, we provide a positive answer to the problem of whether N -qubit pure quantum states exist in which all k -body reduced density are maximally mixed for ##IMG## [http://ej.iop.org/images/1751-8121/54/1/015305/aabc9a4ieqn1.gif] {$k{< }\lfloor \frac{N}{2}\rfloor $} in [1]. In addition, for k ⩾ 4 and any d , there exists an integer N 0 ( k , d ) such that whenever N ⩾ N 0 ( k , d ), we can

Anomalous diffusion phenomena are observed in many areas of interest. They manifest themselves in deviations from the laws of Brownian motion (BM), e.g. in the non-linear growth (mostly power-law) in time of the ensemble average mean squared displacement (MSD). When we analyze the real-life data in the context of anomalous diffusion, the primary problem is the proper identification of the type of the

We study the symmetry resolved entanglement entropies in one-dimensional systems with boundaries. We provide some general results for conformal invariant theories and then move to a semi-infinite chain of free fermions. We consider both an interval starting from the boundary and away from it. We derive exact formulas for the charged and symmetry resolved entropies based on theorems and conjectures

A proof that strong solutions of the Dullin–Gottwald–Holm equation vanishing on an open set of the (1 + 1) space-time are identically zero is presented. In order to do it, we use a geometrical approach based on the conserved quantities of the equation to prove a unique continuation result for its solutions. We show that this idea can be applied to a large class of equations of the Camassa–Holm type

We develop a formalism to compute the statistics of the second largest eigenpair of weighted sparse graphs with N ≫ 1 nodes, finite mean connectivity and bounded maximal degree, in cases where the top eigenpair statistics is known. The problem can be cast in terms of optimisation of a quadratic form on the sphere with a fictitious temperature, after a suitable deflation of the original matrix model

While dealing with the constant-strength magnetic Laplacian on the annulus, we complete Peetre’s work. In particular, the eigenspaces associated with its discrete spectrum true turns out to be polyanalytic spaces with respect to the invariant Cauchy–Riemann operator, and we write down explicit formulas for their reproducing kernels. When the magnetic field strength is an integer, we compute the limits

In this work, we introduce a new realization of exactly-solvable time-dependent Hamiltonians based on the solutions of the fourth Painlevé and the Ermakov equations. The latter is achieved by introducing a shape-invariant condition between an unknown quantum invariant and a set of third-order intertwining operators with time-dependent coefficients. New quantum invariants are constructed after adding

In this work, we introduce a three-stroke quantum engine with a single-qubit working substance whose cycle consists of two strokes arise due to performing two distinct general quantum measurements and it is completed by thermalization through contact with a finite temperature thermal reservoir. It is demonstrated that energy is imported into the engine by first measurement channel and work (useful

An exact representation of the Baker–Campbell–Hausdorff formula as a power series in just one of the two variables is constructed. Closed form coefficients of this series are found in terms of hyperbolic functions, which contain all of the dependence on the second variable. It is argued that this exact series may then be truncated and be expected to give a good approximation to the full expansion if

Construction of superintegrable systems based on Lie algebras have been introduced over the years. However, these approaches depend on explicit realisations, for instance as a differential operators, of the underlying Lie algebra. This is also the case for the construction of their related symmetry algebra which take usually the form of a finitely generated quadratic algebra. These algebras often display

We study the average skew information-based coherence for both random pure and mixed states. The explicit formulae of the average skew information-based coherence are derived and shown to be the functions of the dimension N of the state space. We demonstrate that as N approaches to infinity, the average coherence is 1 for random pure states, and a positive constant less than 1/2 for random mixed states

We describe the contribution of diffractive orbits to semiclassical approximations of Wigner function propagators. These contributions are based on diffractively scattered rays used in the geometrical theory of diffraction (GTD). They provide an extension of well-established approximations of Wigner-function propagators based on rays that propagate by specular reflection and refraction. The wider aim

This article is dedicated to the following class of problems. Start with an N × N Hermitian matrix randomly picked from a matrix ensemble—the reference matrix. Applying a rank- t perturbation to it, with t taking the values 1 ⩽ t ⩽ N , we study the difference between the spectra of the perturbed and the reference matrices as a function of t and its dependence on the underlying universality class of

We extend the investigation of three-dimensional Hamiltonian systems of non-subgroup type admitting non-zero magnetic fields and an axial symmetry, namely the circular parabolic case, the oblate spheroidal case and the prolate spheroidal case. More precisely, we focus on linear and some special cases of quadratic superintegrability. In the linear case, no new superintegrable system arises. In the quadratic

Upper and lower estimates of eigenvalues of the Laplacian on a metric graph have been established in 2017 by Berkolaiko, Kennedy, Kurasov, and Mugnolo. Both these estimates can be achieved at the same time only by highly degenerate eigenvalues which we call maximally degenerate . By comparison with the maximal eigenvalue multiplicity proved by Kac and Pivovarchik in 2011, we characterize the graphs

We identify the ground-state of a truncated version of Haldane’s pseudo-potential Hamiltonian in the thin cylinder geometry as being composed of exponentially many fragmented matrix product states. These states are constructed by lattice tilings and their properties are discussed. We also report on a proof of a spectral gap, which implies the incompressibility of the underlying fractional quantum Hall

We consider a particle diffusing outside a compact planar set and investigate its boundary local time ℓ t , i.e., the rescaled number of encounters between the particle and the boundary up to time t . In the case of a disk, this is also the (rescaled) number of encounters of two diffusing circular particles in the plane. For that case, we derive explicit integral representations for the probability

We compute simultaneously the translational speed, the magnitude and the phase of a quantum vortex ring for a wide range of radii, within the Gross–Pitaevskii model, by imposing its self preservation in a co-moving reference frame. By providing such a solution as the initial condition for the time-dependent Gross–Pitaevskii equation, we verify a posteriori that the ring’s radius and speed are well

We revisit the problem of computing the boundary density profile of a droplet of two-dimensional one-component plasma (2D OCP) with logarithmic interaction between particles in a confining harmonic potential. At a sufficiently low temperature, but still in the liquid phase, the density exhibits oscillations as a function of the distance to the boundary of the droplet. We obtain the density profile

It is shown that planar quantum dynamics can be related to three-body quantum dynamics in the space of relative motion with a special class of potentials. As an important special case the O ( d ) symmetry reduction from d degrees of freedom to one degree is presented. A link between two-dimensional (super-integrable) systems and three-body (super-integrable) systems is revealed. As illustration we

The main characteristics (stationary probability distribution and mean first passage time, MFPT) of random walks on the nodes of a (semi)infinite chain with resetting are obtained. It is shown that their dependences on the resetting rate frequency r essentially differ from those within the classical continuous diffusion model. The same is true for a finite chain in which the existence of an optimal

Let H be a finite-dimensional Hilbert space, dim H ⩾ 2. We prove that every continuous coexistency preserving map on the effect algebra E ( H ) is either a standard automorphism of E ( H ), or a standard automorphism of E ( H ) composed with the orthocomplementation. We present examples showing the optimality of the result.