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This paper continues the investigations of noncommutative ordered spaces put forward by one of the authors. These metaphoric spaces are defined dually by the so-called isocones which generalize to the noncommutative setting the convex cones of orderpreserving functions. In this paper we will consider the case of isocones inside almostcommutative algebras of the form C(M) ⊗ Af, with M a compact metrizable space. We will give a family of isocones in such an algebra with the property that every possible isocone is contained in exactly one member of the family. We conjecture that this family is in fact a complete classification, a hypothesis related with the noncommutative Stone-Weierstrass conjecture. We also obtain that every isocone in C(M) ⊗ Af, with Af noncommutative, induces an order relation on M with the property that every point in M lies in a neighbourhood of incomparable points. Thus, if the causal order relation on spacetime is induced by an isocone in an almost-commutative (but not commutative) algebra, then causality must disappear at small scale. The usual Lorentzian causality would then only arise as an approximation of this noncommutative causality. [ABSTRACT FROM AUTHOR]

In this paper, motivated by Guo [Commun. Math. Phys. 218(2), 293-313 (2001)], we construct the global classical solution to the inelastic Boltzmann equation with potential force by using the standard contraction mapping theorem. Moreover, the dispersion estimates of the solution are obtained. [ABSTRACT FROM AUTHOR]

We classify (m + n)D warped product spaces (¯M , ¯g) satisfying Einstein's equation ¯G = ¯⋀ ¯g.We showthat thewarping function f can determine not only the cosmological constant ¯⋀ but also the cosmological constant ⋀ appearing in induced Einstein's equation G= -⋀h on (M2, h). Moreover, we discuss the origin of the 4D cosmological constant as an emergent effect of higher dimensional warped spaces. [ABSTRACT FROM AUTHOR]

A technique is introduced which allows to generate--starting from any solvable discrete-time dynamical system involving N time-dependent variables--new, generally nonlinear, generations of discrete-time dynamical systems, also involving N time-dependent variables and being as well solvable by algebraic operations (essentially by finding the N zeros of explicitly known polynomials of degree N). The dynamical systems constructed using this technique may also feature large numbers of arbitrary constants, and they need not be autonomous. The solvable character of these models allows to identify special cases with remarkable time evolutions: for instance, isochronous or asymptotically isochronous discrete-time dynamical systems. The technique is illustrated by a few examples. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate that by using a mathematical physics approach--focusing attention on the physics and using mathematics as a tool--it is possible to visualize the formation of the transverse modes inside a cylindrical waveguide. The opposite (physical mathematics) approach looks at the mathematical problem and then tries to impose a physical interpretation. For cylindrical waveguides, the physical mathematics route leads to the Bessel differential equation, and it is argued that in the core of the waveguide there are only Bessel functions of the first kind in the description of the transverse modes. The Neumann functions are deemed non-physical due to their singularity at the origin and are eliminated from the final description of the solution. In this paper, by combining geometric optics and wave optics concepts, we show that the inclusion of the Neumann function is physically necessary to describe fully and properly the formation of the propagating transverse modes. With this approach, we also show that the field outside a dielectric waveguide arises in a natural way. [ABSTRACT FROM AUTHOR]

The purpose of this research is to determine whether the acoustic properties of polydisperse fibrous medium (PDFM) and bidisperse fibrous medium (BDFM) can be modeled by monodisperse fiber media (MDFM) with an effective fiber diameter. Multi-scale numerical simulations on representative elementary volumes of these media are performed to retrieve the transport and geometrical properties governing their acoustic properties. Results show no significant difference between predictions obtained by PDFM or BDFM, and their corresponding effective MDFM. [ABSTRACT FROM AUTHOR]

We present a bilinear Hirota representation of the N = 2 supersymmetric extension of the Korteweg-de Vries equation. This representation is deduced using binary Bell polynomials, hierarchies, and fermionic limits. We, also, propose a new approach for the generalisation of the Hirota bilinear formalism in the N = 2 supersymmetric context. [ABSTRACT FROM AUTHOR]

We analyze the dynamics of the AdSN+1 particle realized on the coset SO(2,N)/SO (1,N). Hamiltonian reduction provides the physical phase space in terms of the coadjoint orbit obtained by boosting a timelike element of so(2,N). We show equivalence of this approach to geometric quantization and to the SO(N) covariant oscillator description, for which the boost generators entail a complicated operator ordering. As an alternative scheme, we introduce dual oscillator variables and derive their algebra at the classical and the quantum levels. This simplifies the calculations of the commutators for the boost generators and leads to unitary irreducible representations of so(2,N) for all admissible values of the mass parameter. We furthermore discuss an SO(N) covariant supersymmetric extension of the oscillator quantization, with its realization for superparticles in AdS2 and AdS3 given by recent works. [ABSTRACT FROM AUTHOR]

Let A be a unital C*-algebra and let σ be a one-parameter automorphism group of A. We consider QSSσ (A), the set of all quantum symmetric states on *1∞ A that are also KMS states (for a fixed inverse temperature, for specificity taken to be -1) for the free product automorphism group *1∞ σ. We characterize the elements of QSSσ (A), we show that QSSσ (A) is a Choquet simplex whenever it is nonempty and we characterize its extreme points. [ABSTRACT FROM AUTHOR]

Energy balance equation for steady state Sweet-Parker reconnection in a relativistic regime is reanalyzed, employing a complete electromagnetic energy equation. A correction related to Vin is added with electric energy taken into account. The validity and meaning of the correction are demonstrated with the energy-momentum tensor. Predictions of the new scaling are compared with the previous ones. Energy calculation is also used in the cases with guide field, with a view to the role of the guide field for energy balance. And the relativistic tearing mode growth rate with guide field is discussed using the fluid model. [ABSTRACT FROM AUTHOR]

Local configurations of three-dimensional magnetic nulls with pure second order expansions are investigated, both potentially and nonpotentially. The basic magnetic structures are classified and visualized according to the configurations of their electric current, which is of first order. A principle of constructing a 2nd order null is proposed. [ABSTRACT FROM AUTHOR]

His physics culture interjections and jokes enhance his presentation. Http://physicswithelliot.com https://tinyurl.com/WS-pwe5methods https://tinyurl.com/WS-pwedimanalysis https://tinyurl.com/WS-pweCheck Dr. Elliot Schneider's didactic YouTube channel on introductory mathematics for physicists seems nicely targeted for bachelors physics students, particularly due to his physics framing and "reading ahead" discussion of math approaches and extensions to come in upper division courses. He has a second video on using practical dimensional analysis focused on only introductory mechanics in I What I Wish I'd Known As A Beginning Physics Student i . [Extracted from the article]

Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ reversible Markov chains. Reversible chains obey detailed balance and thus ensure that the system will eventually relax to equilibrium, though detailed balance is not necessary for convergence to equilibrium. We review nonreversible Markov chains, which violate detailed balance and yet still relax to a given target stationary distribution. In particular cases, nonreversible Markov chains are substantially better at sampling than the conventional reversible Markov chains with up to a square root improvement in the convergence time to the steady state. One kind of nonreversible Markov chain is constructed from the reversible ones by enlarging the state space and by modifying and adding extra transition rates to create non-reversible moves. Because of the augmentation of the state space, such chains are often referred to as lifted Markov Chains. We illustrate the use of lifted Markov chains for efficient sampling on several examples. The examples include sampling on a ring, sampling on a torus, the Ising model on a complete graph, and the one-dimensional Ising model. We also provide a pseudocode implementation, review related work, and discuss the applicability of such methods. [ABSTRACT FROM AUTHOR]

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the wellestablished theory of equilibrium statistical mechanics. [ABSTRACT FROM AUTHOR]

This paper is devoted to the construction of what we will call exactly solvable models, i.e., of quantum mechanical systems described by an Hamiltonian H whose eigenvalues and eigenvectors can be explicitly constructed out of some minimal ingredients. In particular, motivated by PT-quantum mechanics, we will not insist on any self-adjointness feature of the Hamiltonians considered in our construction. We also introduce the so-called bicoherent states, we analyze some of their properties and we show how they can be used for quantizing a system. Some examples, both in finite and in infinite-dimensional Hilbert spaces, are discussed. [ABSTRACT FROM AUTHOR]

Recent studies have shown that the entropy production rate for the master equation consists of two non-negative terms: the adiabatic and non-adiabatic parts, where the non-adiabatic part is also known as the free energy dissipation rate. In this paper, we present some nonzero lower bounds for the free energy, the entropy production rate, and its adiabatic and non-adiabatic parts. These nonzero lower bounds not only reveal some novel dissipative properties for nonequilibrium dynamics which are much stronger than the second law of thermodynamics, but also impose some new constraints on thermodynamic constitutive relations. Moreover, we also give a mathematical application of the nonzero lower bounds by studying the long-time behavior of the master equation. Extensions to the Tsallis statistics are also discussed, including the nonzero lower bounds for the Tsallis-type free energy and its dissipation rate. [ABSTRACT FROM AUTHOR]

The weak coupling asymptotics to order of the ground state energy of the delta-function Fermi gas, derived heuristically in the literature, is here made rigorous. Further asymptotics are in principle computable. The analysis applies to the Gaudin integral equation, a method previously used by one of the authors for the asymptotics of large Toeplitz matrices. [ABSTRACT FROM AUTHOR]

We consider the Cauchy problem for the L²-critical focussing nonlinear Schrödinger equation with a fractional dissipation. According to the order of the fractional dissipation, we prove the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed for... . [ABSTRACT FROM AUTHOR]

The article highlights importance of geometric mean. It mentions solution of a physical problem by computing the geometric mean of two relevant scales and presents several example including measurement of distance to the horizon when lifeguard sitting in a high chair; measurement of spin down time while stirring tea; and for calculation of resonant LRC circuit (an inductor L , resistor R, and a capacitor C).

Illustrations provided byDaniel Murrell, dansmurrell@gmail.com When I began teaching high school physics, I found that many of my students were not just struggling with the mathematics of physics but the way the language was used. Physics is sometimes discussed as being a second language where common words are coded with specific alternate definitions (consider how you use the word "delta"). Furthermore, many of our students are English Language Learners. Thus, providing developmentally appropriate assistance to building scientific vocabulary not only addresses equity issues but can be a highly effective teaching strategy. In this article, I provide an example of one such approach to addressing literacy issues: a vocabulary building story on Convection, Conduction, and Radiation. [ABSTRACT FROM AUTHOR]

Velocity reciprocity and the relativity principle Patrick Moylan B 90 b (2), p. 126 https://doi.org/10.1119/10.0009219 Velocity reciprocity is the property that pairs of inertial reference frames will measure each other to have equal and opposite relative velocities. This paper analyses the group-theoretic foundations of relativity theory to explore what additional assumptions must be made for velocity reciprocity to hold, and also explores the misconception that velocity reciprocity follows from the relativity of motion principle. Exploring complex pattern formation with convolutional neural networks Christian Scholz and Sandy Scholz B 90 b (2), p. 141 https://doi.org/10.1119/5.0065458 Machine learning is becoming more and more important in the analysis of data in many fields including physics. [Extracted from the article]

The viscosity affects the rate at which air flows through a tube (Poiseuille flow), but both the applied pressure and the flow rate must be accurately measured. Yet another approach to solutions of one-dimensional wave equations with inhomogeneous bounda... Qiong-Gui Lin B 90 b (1), p. 31 https://doi.org/10.1119/5.0058957 Solving the wave equation or the diffusion equation (in one or more dimensions) with appropriate boundary and initial conditions is one of the basic problems in mathematical physics. This approach couples nicely to concepts typically included in the introductory physics sequence, making the Clausius-Clapeyron equation accessible to beginning students. [Extracted from the article]

We study the symmetry group properties of the variable coefficient Davey-Stewartson (vcDS) system. The Lie point symmetry algebra with a Kac-Moody-Virasoro (KMV) structure is shown to be isomorphic to that of the usual (constant coefficient) DS system if and only if the coefficients satisfy some conditions. These conditions turn out to coincide with those for the vcDS system to be transformable to the DS system by a point transformation. The equivalence group of the vcDS system is applied to pick out the integrable subsystems from a class of non-integrable ones. Additionally, the full symmetry group of the DS system is derived explicitly without exponentiating its symmetry algebra. Lump solutions (rationally localized in all directions in R²) introduced by Ozawa for the DS system are shown to hold even for the vcDS system precisely when the system belongs to the integrable class, i.e., equivalent to the DS system. These solutions can be used for establishing exact blow-up solutions in finite time in the space L²(R²) in the focusing case. [ABSTRACT FROM AUTHOR]

A functional realization of the Lie algebra sl (3,R) as a Vessiot-Guldberg-Lie algebra of second order differential equation (SODE) Lie systems is proposed. It is shown that a minimal Vessiot-Guldberg-Lie algebra LVG is obtained from proper subalgebras of sl (3,R) for each of the SODE Lie systems of this type by particularization of one functional and two scalar parameters of the sl (3,R)-realization. The relation between the various Vessiot-Guldberg-Lie algebras by means of a limiting process in the scalar parameters further allows to define a notion of contraction of SODE Lie systems. [ABSTRACT FROM AUTHOR]

Using a Krein indefinite metric in Fock space, the Hamiltonian for cut-off models of canonically quantized Higgs-Yang-Mills fields interpolating between the Gupta-Bleuler-Feynman and Landau gauges is shown to be essentially maximal accretive and essentially Krein selfadjoint. [ABSTRACT FROM AUTHOR]

In this paper we propose versions of the associative Yang-Baxter equation and higher order R-matrix identities which can be applied to quantum dynamical R-matrices. As is known quantum non-dynamical R-matrices of Baxter-Belavin type satisfy this equation. Together with unitarity condition and skew-symmetry it provides the quantum Yang-Baxter equation and a set of identities useful for different applications in integrable systems. The dynamical R-matrices satisfy the Gervais-Neveu-Felder (or dynamical Yang-Baxter) equation. Relation between the dynamical and nondynamical cases is described by the IRF (interaction-round-a-face)-Vertex transformation. An alternative approach to quantum (semi-)dynamical R-matrices and related quantum algebras was suggested by Arutyunov, Chekhov, and Frolov (ACF) in their study of the quantum Ruijsenaars-Schneider model. The purpose of this paper is twofold. First, we prove that the ACF elliptic R-matrix satisfies the associative Yang-Baxter equation with shifted spectral parameters. Second, we directly prove a simple relation of the IRF-Vertex type between the Baxter-Belavin and the ACF elliptic R-matrices predicted previously by Avan and Rollet. It provides the higher order R-matrix identities and an explanation of the obtained equations through those for non-dynamical R-matrices. As a by-product we also get an interpretation of the intertwining transformation as matrix extension of scalar theta function likewise Rmatrix is interpreted as matrix extension of the Kronecker function. Relations to the Gervais-Neveu-Felder equation and identities for the Felder's elliptic R-matrix are also discussed. [ABSTRACT FROM AUTHOR]

Shannon's entropy power inequality (EPI) can be viewed as a statement of concavity of an entropic function of a continuous random variable under a scaled addition rule: f (√a X + √1 - a Y) ≥ a f (X) + (1 - a) f (Y) ∀ a ∊ [0,1]. Here, X and Y are continuous random variables and the function f is either the differential entropy or the entropy power. König and Smith [IEEE Trans. Inf. Theory 60(3), 1536-1548 (2014)] and De Palma, Mari, and Giovannetti [Nat. Photonics 8(12), 958-964 (2014)] obtained quantum analogues of these inequalities for continuous-variable quantum systems, where X and Y are replaced by bosonic fields and the addition rule is the action of a beam splitter with transmissivity a on those fields. In this paper, we similarly establish a class of EPI analogues for d-level quantum systems (i.e., qudits). The underlying addition rule for which these inequalities hold is given by a quantum channel that depends on the parameter a ∊ [0,1] and acts like a finite-dimensional analogue of a beam splitter with transmissivity a, converting a two-qudit product state into a single qudit state. We refer to this channel as a partial swap channel because of the particular way its output interpolates between the states of the two qudits in the input as a is changed from zero to one. We obtain analogues of Shannon's EPI, not only for the von Neumann entropy and the entropy power for the output of such channels, but also for a much larger class of functions. This class includes the Rényi entropies and the subentropy. We also prove a qudit analogue of the entropy photon number inequality (EPnI). Finally, for the subclass of partial swap channels for which one of the qudit states in the input is fixed, our EPIs and EPnI yield lower bounds on the minimum output entropy and upper bounds on the Holevo capacity. [ABSTRACT FROM AUTHOR]

Entanglement is a resource to overcome the natural restriction of operations used for state manipulation to Local Operations assisted by Classical Communication (LOCC). Hence, a bipartite maximally entangled state is a state which can be transformed deterministically into any other state via LOCC. In the multipartite setting no such state exists. There, rather a whole set, the Maximally Entangled Set of states (MES), which we recently introduced, is required. This set has on the one hand the property that any state outside of this set can be obtained via LOCC from one of the states within the set and on the other hand, no state in the set can be obtained from any other state via LOCC. Recently, we studied LOCC transformations among pure multipartite states and derived the MES for three and generic four qubit states. Here, we consider the non-generic four qubit states and analyze their properties regarding local transformations. As already the most coarse grained classification, due to Stochastic LOCC (SLOCC), of four qubit states is much richer than in case of three qubits, the investigation of possible LOCC transformations is correspondingly more difficult. We prove that most SLOCC classes show a similar behavior as the generic states, however we also identify here three classes with very distinct properties. The first consists of the GHZ and W class, where any state can be transformed into some other state non-trivially. In particular, there exists no isolation. On the other hand, there also exist classes where all states are isolated. Last but not least we identify an additional class of states, whose transformation properties differ drastically from all the other classes. Although the possibility of transforming states into local-unitary inequivalent states by LOCC turns out to be very rare, we identify those states (with exception of the latter class) which are in the MES and those, which can be obtained (transformed) non-trivially from (into) other states respectively. These investigations do not only identify the most relevant classes of states for LOCC entanglement manipulation, but also reveal new insight into the similarities and differences between separable and LOCC transformations and enable the investigation of LOCC transformations among arbitrary four qubit states. [ABSTRACT FROM AUTHOR]

We extend the result on the symmetry of quantum torus by Rieffel and Schwarz to the symmetry of quantum supertorus. The symmetry group is extended from O(n,n,Z) to OSp(n,n∣2m,Z). [ABSTRACT FROM AUTHOR]

We construct the inverse Shapovalov form of a simple complex quantum group from its universal R-matrix based on a generalized Nagel-Moshinsky approach to lowering operators. We establish a connection between this algorithm and the ABRR equation for dynamical twist. [ABSTRACT FROM AUTHOR]

Regular polygon periodic solutions of the Coulomb equation of motion for a system of n + 2 charges, in which equal n - 1 negative charges and one positive charge are restricted to a plane, are found. They are such that the coordinates of the equal planar charges coincide with vertices of a regular polygon centered at the origin where the immobile positive charge is located. The simplest of them are exact solutions which describe a rotation of the planar equal negative charges around the positive charge. The exact solutions are characterized by immobile non-planar two equal charges, which are located at the perpendicular crossing the origin, whose distances to it are equal. [ABSTRACT FROM AUTHOR]

We study the necessary conditions for preserving N = (4,4) supersymmetry on curved 2d backgrounds, following the strategy of Dumitrescu, Festuccia, and Seiberg. We derive the transformation laws and invariant action for offshell Abelian vector multiplets. An explicit solution of the supersymmetry conditions is found on the round two-sphere. [ABSTRACT FROM AUTHOR]