The quantum vacuum (Casimir) energy arising from noninteracting massless quanta is known to induce a long-range force, while decays exponentially for massive fields and separations larger than the inverse mass of the quanta involved. Here, we show that the interplay between dimensionality and nonlinearities in the field theory alters this behaviour in a nontrivial way. We argue that the changes are

In the ballistic regime we study both semiclassically and quantum mechanically the electron’s dynamics in two-dimensional electron gas in the presence of an inhomogeneous magnetic field applied perpendicular to the plane. The magnetic field is constant inside four separate circular regions which are located at the four corners of a square of side length larger than the diameter of the circles, while

As is known, the irreducible projective representations (Reps) of anti-unitary groups contain three different situations, namely, the real, the complex and quaternionic types with torsion number 1, 2, 4 respectively. This subtlety increases the complexity in obtaining irreducible projective Reps of anti-unitary groups. In the present work, a physical approach is introduced to derive the condition of

Source-free so-called ModMax theories of nonLinear electrodynamics (NLE) in the four dimensional Minkowski spacetime vacuum are the only possible continuous deformations—and as a function of a single real and positive parameter—of source-free Maxwell linear electrodynamics (MLE) in the same vacuum, which preserve all the same Poincar and conformal spacetime symmetries as well as the continuous duality

This paper is to evaluate certain Catalan-Hankel Pfaffians by the theory of skew orthogonal polynomials. Due to different kinds of hypergeometric orthogonal polynomials underlying the Askey scheme, we explicitly construct the classical skew orthogonal polynomials and then give different examples of Catalan-Hankel Pfaffians with continuous and q-moment sequences.

The problem of quantizing a particle on a two-sphere has been treated by numerous approaches, including Isham’s global method based on unitary representations of a symplectic symmetry group that acts transitively on the phase space. Here we reconsider this simple model using Isham’s scheme, enriched by a magnetic flux through the sphere via a modification of the symplectic form. To maintain complete

The linear stability of double rows of equidistant point vortices for an inviscid generalized two-dimensional (2D) fluid system is studied. This system is characterized by the relation q = −(Δ) α/2 ψ between the active scalar q and the stream function ψ. Here, α is a positive real number not exceeding 3, and q is referred to as the generalized vorticity. The stability of double rows of equidistant

We revisit the nonequilibrium phase transition between a spatially homogeneous low-density phase and a phase-separated high-density state in the deterministic sublattice totally asymmetric simple exclusion process with stochastic defect. We discuss this phase transition in a grandcanonical ensemble for which we obtain exact results for the stationary current-density correlations and for the average

The random variable 1 + z 1 + z 1 z 2 + … appears in many contexts and was shown by Kesten to exhibit a heavy tail distribution. We consider natural extensions of this variable and its associated recursion to N N matrices either real symmetric β = 1 or complex Hermitian β = 2. In the continuum limit of this recursion, we show that the matrix distribution converges to the inverse-Wishart ensemble of

Consider the statement ‘Every Yang–Baxter integrable system is defined to be exactly-solvable’. To formalise this statement, definitions and axioms are introduced. Then, using a specific Yang–Baxter integrable bosonic system, it is shown that a paradox emerges. A generalisation for completely integrable bosonic systems is also developed.

By using the propagator of linear potential as a main tool, we extend the Airy gas (AG) model, originally developed for the three-dimensional (d = 3) edge electron gas, to systems in reduced dimensions (d = 2, 1). First, we derive explicit expressions for the edge particle density and the corresponding kinetic energy density (KED) of the AG model in all dimensions. The densities are shown to obey the

Losses in quantum communication lines severely affect the rates of reliable information transmission and are usually considered to be state-independent. However, the loss probability does depend on the system state in general, with the polarization dependent losses being a prominent example. Here we analyze biased trace decreasing quantum operations that assign different loss probabilities to states

The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the future tube, seen as an eight-dimensional real manifold, is endowed with a natural positive-definite Riemannian metric that accommodates the underlying geometry of the indefinite Minkowski space metric, together with its symmetry

The Bloch hyperboloid H 2 underlies the quantum geometry of the original SO(2, 1) squeezed states. In Hasebe (2020 J. Phys. A: Math. Theor. 53 055303), the author utilized a non-compact 2nd Hopf map and a Bloch four-hyperboloid H 2,2 to explore an SO(2, 3) extension of the squeezed states. In the present paper, we further pursue the idea to derive an SO(4, 1) version of squeezed vacuum based on the

The effective Hamiltonian for electrons in bilayer graphene with applied magnetic fields is solved through second-order supersymmetric quantum mechanics. This method transforms the corresponding eigenvalue problem into two intertwined one-dimensional stationary Schrdinger equations whose potentials are determined by choosing at most two seed solutions. In this paper new kinds of magnetic fields associated

Variational quantum algorithms rely on gradient based optimization to iteratively minimize a cost function evaluated by measuring output(s) of a quantum processor. A barren plateau is the phenomenon of exponentially vanishing gradients in sufficiently expressive parametrized quantum circuits. It has been established that the onset of a barren plateau regime depends on the cost function, although the

We consider pairwise interaction energies and we investigate their minimizers among lattices with prescribed minimal vectors (length and coordination number), i.e. the one corresponding to the crystal’s bonds. In particular, we show the universal minimality—i.e. the optimality for all completely monotone interaction potentials—of strongly eutactic lattices among these structures. This gives new optimality

We study the discrete spectrum of the two-particle Schrdinger operator , , associated to the Bose–Hubbard Hamiltonian of a system of two identical bosons interacting on site and nearest-neighbor sites in the two dimensional lattice with interaction magnitudes and , respectively. We completely describe the spectrum of and establish the optimal lower bound for the number of eigenvalues of outside its

In recent years, new properties of space-time duality in the Hamiltonian formalism of certain integrable classical field theories have been discovered and have led to their reformulation using ideas from covariant Hamiltonian field theory: in this sense, the covariant nature of their classical r-matrix structure was unravelled. Here, we solve the open question of extending these results to a whole

The aim of this article is to relate the discrete quantum walk on with the continuous Schrdinger operator on in the scattering problem. Each point of is associated with a barrier of the potential, and the coin operator of the quantum walk is determined by the transfer matrix between bases of WKB solutions on the classically allowed regions of both sides of the barrier. This correspondence enables us

Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with the spatial positions of the monomer units. The geometrical patterns of lamellae, hexagonally packed cylinders, and balls arranged in a body-centered cubic lattice

Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical model or class of models of the underlying random walks. Reliable inference is made difficult by the inherent stochastic nature of single particle motion, by experimental

Averaging physical quantities over Lie groups appears in many contexts across the rapidly developing branches of physics like quantum information science or quantum optics. Such an averaging process can be always represented as averaging with respect to a finite number of elements of the group, called a finite averaging set. In the previous research such sets, known as t-designs, were constructed only

Random knot models are often used to measure the types of entanglements one would expect to observe in an unbiased system with some given physical property or set of properties. In nature, macromolecular chains often exist in extreme confinement. Current techniques for sampling random polygons in confinement are limited. In this paper, we gain insight into the knotting behavior of random polygons in

In recent years, instanton calculus has successfully been employed to estimate tail probabilities of rare events in various stochastic dynamical systems. Without further corrections, however, these estimates can only capture the exponential scaling. In this paper, we derive a general, closed form expression for the leading prefactor contribution of the fluctuations around the instanton trajectory for

We investigate the asymptotic behaviour of multi-component links where the edges can be distributed among the components in all possible ways. Specifically we consider a link of k polygons on the simple cubic lattice. We prove two results about the exponential behaviour and use a Monte Carlo method to investigate how the value of the critical exponent depends on link type. One ring grows at the expense

Analytic predictions have been derived recently by Dohm and Wessel (2021 Phys. Rev. Lett. 126 060601) from anisotropic φ 4 theory and conformal field theory for the amplitude of the critical free energy of finite anisotropic systems in the two-dimensional Ising universality class. These predictions employ the hypothesis of multiparameter universality. We test these predictions by means of high-precision

Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the Harper–Hofstadter, the Haldane models, demonstrating one-way waveguides and topologically protected edge states. Central to these discoveries is the chirality induced by

We derive the semi-classical Lindblad master equation in phase space for both canonical and non-canonical Poisson brackets using the Wigner–Moyal formalism and the Moyal star-product. The semi-classical limit for canonical dynamical variables, i.e. canonical Poisson brackets, is the Fokker–Planck equation, as derived before. We generalize this limit and show that it holds also for non-canonical Poisson

In the May–Leonard model of three cyclically competing species, we analyze the statistics of rare events in which all three species go extinct due to strong but rare fluctuations. These fluctuations are from the tails of the probability distribution of species concentrations. They render a coexistence of three populations unstable even if the coexistence is stable in the deterministic limit. We determine

In this work we establish the relation between the Jacobi last multiplier, which is a geometrical tool in the solution of problems in mechanics and that provides Lagrangian descriptions and constants of motion for second-order ordinary differential equations, and nonholonomic Lagrangian mechanics where the dynamics is determined by Hamel’s equations.

We prove that all macroscopic properties of the N-qubit cluster state are asymptotically invariant under local transformations in the limit N ≫ 1, and can be described by a distribution function similar to that of the completely mixed state.

The Kronecker coefficients are the structure constants for the restriction of irreducible representations of the general linear group GL(nm) into irreducibles for the subgroup GL(n) GL(m). In this work we study the quasipolynomial nature of the Kronecker function using elementary tools from polyhedral geometry. We write the Kronecker function in terms of coefficients of a vector partition function

We calculate Wilson loops in lowest order of perturbation theory for triangular contours whose edges are circular arcs. Based on a suitable disentanglement of the relations between metrical and conformal parameters of the contours, the result fits perfectly in the structure predicted by the anomalous conformal Ward identity. The conformal remainder function depends in the generic 4D case on three cusp

We consider the interaction of solitary waves in a model involving the well-known ϕ 4 Klein–Gordon theory, but now bearing both Laplacian and biharmonic terms with different prefactors. As a result of the competition of the respective linear operators, we obtain three distinct cases as we vary the model parameters. In the first the biharmonic effect dominates, yielding an oscillatory inter-wave interaction;

Using recently developed Seifert fibering operators for 3D gauge theories, we formulate the necessary ingredients for a state-integral model of the topological quantum field theory dual to a given Seifert manifold under the 3D–3D correspondence, focusing on the case of Seifert homology spheres with positive orbifold Euler characteristic. We further exhibit a set of difference operators that annihilate

Resource theories are broad frameworks that capture how useful objects are in performing specific tasks. In this paper we devise a formal resource theory quantum measurements, focusing on the ability of a measurement to acquire information. The objects of the theory are equivalence classes of positive operator-valued measures, and the free transformations are changes to a measurement device that can

Inspired by G Frieden’s recent work on the geometric R-matrix for affine type A crystal associated with rectangular shaped Young tableaux, we propose a method to construct a novel family of discrete integrable systems which can be regarded as a geometric lifting of the generalized periodic box–ball systems. By converting the conventional usage of the matrices for defining the Lax representation of

We show that the configuration in the phase space of the elliptic Calogero–Moser model when particles stick together in pairs is stable under the third Hamiltonian flow of the model. The equations of motion for the pairs coincide with the equations of motion for poles of elliptic solutions to the B-version of the Kadomtsev–Petviashvili equation.

We formulate Dp-brane Newton–Cartan (NC) background through the limiting procedure from relativistic Dirac–Born–Infeld action and Wess–Zumino term. We also determine action for unstable D(p + 1)-brane in Dp-brane NC background and study its properties.

Mathematical analysis of quantum control landscapes, which aims to prove either absence or existence of traps for quantum control objective functionals, is an important topic in quantum control. In this work, we provide a rigorous analysis of quantum control landscapes for ultrafast generation of single-qubit quantum gates and show, combining analytical methods based on a sophisticated analysis of

Entanglement is one of essential quantum resources in quantum information processing, playing an important role during quantum communication and computation. While any system unavoidably interacts with its surrounding environment, this thus will result in decoherence or dissipation effect. With this in mind, a natural question arises: how to recover quantum entanglement under decoherence inducing by

We obtain exact densities of contractible and non-contractible loops in the O(1) model on a strip of the square lattice rolled into an infinite cylinder of finite even circumference L. They are also equal to the densities of critical percolation clusters on 45 degree rotated square lattice rolled into a cylinder, which do not or do wrap around the cylinder respectively. The results are presented as

Modular graph forms (MGFs) are a class of non-holomorphic modular forms which naturally appear in the low-energy expansion of closed-string genus-one amplitudes and have generated considerable interest from pure mathematicians. MGFs satisfy numerous non-trivial algebraic- and differential relations which have been studied extensively in the literature and lead to significant simplifications. In this

Motivated by a range of biological applications related to the transport of molecules in cells, we present a modular framework to treat first-passage problems for diffusion in partitioned spaces. The spatial domains can differ with respect to their diffusivity, geometry, and dimensionality, but can also refer to transport modes alternating between diffusive, driven, or anomalous motion. The approach

In this paper, we first try to shed light on the ambiguities that exist in the literature in the generalization of the standard linear response theory (LRT) which has been basically formulated for closed systems to the theory of open quantum systems in the Heisenberg picture. Then, we investigate the linear response of a driven-dissipative optomechanical system (OMS) to a weak time-dependent perturbation

A class of models is considered for a quantum particle constrained on degenerate Riemannian manifolds known as Grushin cylinders, and moving freely subject only to the underlying geometry: the corresponding spectral and scattering analysis is developed in detail in view of the phenomenon of transmission across the singularity that separates the two half-cylinders. Whereas the classical counterpart

Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions provide us with the solutions of various hydrodynamic type equations. Integrable one dimensional systems in terms of Riemann invariants and its extensions, multidimensional equations describing isoenthalpic and polytropic motions

We propose an approach to process data from interferometric measurements on a closed quantum system at random times. For this purpose a time correlation matrix is introduced which enables us to extract dynamical properties of the quantum system. After defining a generalized expectation value we obtain a distribution of time scales, an average transition time and a correlation time. A classical limit

The modular operator approach of Tomita–Takesaki to von Neumann algebras is elucidated in the algebraic structure of certain supersymmetric (SUSY) quantum mechanical systems. A von Neumann algebra is constructed from the operators of the system. An explicit operator characterizing the dual infinite degeneracy structure of a SUSY two dimensional system is given by the modular conjugation operator. Furthermore

Trajectory-based methods are well-developed to approximate steady-state probability distributions for stochastic processes in large-system limits. The trajectories are solutions to equations of motion of Hamiltonian dynamical systems, and are known as eikonals. They also express the leading flow lines along which probability currents balance. The existing eikonal methods for discrete-state processes

We study possible geometries and R-symmetry breaking patterns that lead to globally BPS surface operators in the six dimensional theory. We find four main classes of solutions in different subspaces of and a multitude of subclasses and specific examples. We prove that these constructions lead to supersymmetry preserving observables and count the number of preserved supercharges. We discuss the underlying

Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a set of classical particles. Here we consider the evolution of symmetrized moments for free particles in one dimension, first examining the geometric properties of

Port-based teleportation (PBT) is a teleportation protocol that employs a number of Bell pairs and a joint measurement to enact an approximate input-output identity channel. Replacing the Bell pairs with a different multi-qubit resource state changes the enacted channel and allows the PBT protocol to simulate qubit channels beyond the identity. The channel resulting from PBT using a general resource

The formalism for Poisson–Hopf (PH) deformations of Lie–Hamilton (LH) systems, recently proposed in Ballesteros etal (2018 J. Phys. A: Math. Theor. 51 065202), is refined in one of its crucial points concerning applications, namely the obtention of effective and computationally feasible PH deformed superposition rules for prolonged PH deformations of LH systems. The two new notions here proposed are

In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable lattices admit two hierarchies of generalized symmetries corresponding to the discrete and continuous independent variables n and x. Symmetries corresponding to the

A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is given, involving the expectation values of functionals of solution to the SDE and a reconstruction theorem for general stochastic symmetries is proved. Moreover, the notable case of reduction under the closed

We identify the self-similarity limit of the second flow of sl(N) mKdV hierarchy with the periodic dressing chain thus establishing a connection to invariant Painlev equations. The Bcklund symmetries of dressing equations and Painlev equations are obtained in the self-similarity limit of gauge transformations of the mKdV hierarchy realized as zero-curvature equations on the loop algebra endowed with

In the present article, we consistently develop the main issues of the Bloch vectors formalism for an arbitrary finite-dimensional quantum system. In the frame of this formalism, qudit states and their evolution in time, qudit observables and their expectations, entanglement and nonlocality, etc are expressed in terms of the Bloch vectors—the vectors in the Euclidean space , arising under decompositions

Completing a Swiss-cheese theorem of Lieb and Lebowitz (LL), we prove that any population of spheres with power-law radius distribution can completely fill 3D Euclidean space if the exponent is such that 2.8 ⩽ d f < 3. This sufficient condition extends considerably the known part of the ensemble of space-filling populations of polydisperse spheres. The self-similar spatial arrangement of the polydisperse