Letters in Mathematical Physics最新文献

Nozaki et al. gave a homotopy classification of the knotted defects of ordered media in three-dimensional space by considering continuous maps from complements of spatial graphs to the order parameter space modulo a certain equivalence relation. We extend their result by giving a classification scheme for ordered media in handlebodies, where defects are allowed to reach the boundary. Through monodromies around meridional loops, global defects are described in terms of planar diagrams whose edges are colored by elements of the fundamental group of the order parameter space. We exhibit examples of this classification in octahedral frame fields and biaxial nematic liquid crystals.

Breathers have been experimentally and theoretically found in many physical systems—in particular, in integrable nonlinear-wave models. A relevant problem is to study the breather gas, which is the limit, for (Nrightarrow infty ), of N-breather solutions. In this paper, we investigate the breather gas in the framework of the focusing nonlinear Schrödinger (NLS) equation with nonzero boundary conditions, using the inverse scattering transform and Riemann–Hilbert problem. We address aggregate states in the form of N-breather solutions, when the respective discrete spectra are concentrated in specific domains. We show that the breather gas coagulates into a single-breather solution whose spectral eigenvalue is located at the center of the circle domain, and a multi-breather solution for the higher-degree quadrature concentration domain. These coagulation phenomena in the breather gas are called breather shielding. In particular, when the nonzero boundary conditions vanish, the breather gas reduces to an n-soliton solution. When the discrete eigenvalues are concentrated on a line, we derive the corresponding Riemann–Hilbert problem. When the discrete spectrum is uniformly distributed within an ellipse, it is equivalent to the case of the line domain. These results may be useful to design experiments with breathers in physical settings.

String-localized QFT allows to explain Standard Model interactions in an autonomous way, committed to quantum principles rather than a “gauge principle,” thus avoiding an indefinite state space and compensating ghosts. The resulting perturbative scattering matrix is known (at tree-level and without spacetime cutoff) to be insensitive to the non-locality of the auxiliary “string-localized free fields” used in the construction. For the examples of Yang–Mills and QCD, we prove that it is equivalent to the perturbative S-matrix of gauge theory, restricted to physical particle states. The role of classical gauge invariance is revealed along the way. The main tool are “dressed fields,” that are intermediate between free fields and interacting fields, and for which we give explicit formulas at all orders. The renormalization of loops, as well as non-perturbative issues are not addressed, but we hint at the possibility, enabled by our approach, that qualitative traces of confinement may be visible already at the level of the dressed fields.

We consider the homogeneous Bose gas in the three-dimensional unit torus, where N particles interact via a two-body potential of the form (N^{-1} v(x)). The system is studied at inverse temperatures of order (N^{-2/3}), which corresponds to the temperature scale of the Bose–Einstein condensation phase transition. We show that spontaneous U(1) symmetry breaking occurs if and only if the system exhibits Bose–Einstein condensation in the sense that the one-particle density matrix of the Gibbs state has a macroscopic eigenvalue.

In this paper, we describe the actions of standard generators on certain bases of simple modules for semisimple cyclotomic Hecke–Clifford superalgebras. As applications, we explicitly construct a complete set of primitive idempotents and seminormal bases for these algebras.

In this work, we investigate the results regarding the existence and non-existence of non-negative, non-trivial, (C^2)- solutions to the equation

with (n ge 3), (sigma in (0,1)), and (alpha >1). Our choice of this mathematical model, called Lane–Emden–Matukuma equation, is to provide a natural interpolation of the Lane–Emden equation corresponding to the case (sigma =0) and the Matukuma equation corresponding to the case (sigma =1). This is a continuation of our earlier work in which the sublinear case (alpha le 1) was studied. In the supercritical case, namely (alpha >1), we prove that the equation admits non-trivial, non-negative, (C^2)-solution if, and only if,

This provides a comprehensive overview of non-existence and existence results for the equation in the full generality of the parameters (sigma in [0,1]) and (alpha in textbf{R}).

Thanks to an ambitious project initiated by Catino, Mastrolia, Monticelli, and Rigoli, which aims to provide a unified viewpoint for various geometric solitons, many classes, including Ricci solitons, Yamabe solitons, k-Yamabe solitons, quasi-Yamabe solitons, and conformal solitons, can now be studied under a unified framework known as Einstein-type manifolds. Einstein-type manifolds are characterized by four constants, denoted by (alpha , beta , mu ), and (rho ). In this paper, we completely classify all non-trivial, complete gradient Einstein-type Kähler manifolds with (alpha = 0). As a corollary, we obtain rotational symmetry for many classes. In particular, we show that any non-trivial complete quasi-Yamabe gradient soliton on Kähler manifolds is rotationally symmetric.

It is known that the q-deformed Virasoro algebra can be constructed from a certain representation of the quantum toroidal (mathfrak {gl}_1) algebra. In this paper, we apply the same construction to the quantum toroidal algebra of type (mathfrak {gl}_2) and study the properties of resulting generators (W_i(z)) ((i=1,2)). The algebra generated by (W_i(z)) can be regarded as a q-deformation of the direct sum (textsf{F} oplus textsf{SVir}), where (textsf{F}) denotes the free fermion algebra and (textsf{SVir}) stands for the (N=1) super Virasoro algebra, also referred to as the (N=1) superconformal algebra or the Neveu–Schwarz–Ramond algebra. Moreover, the generators (W_i(z)) admit two screening currents, and we show that their degeneration limits coincide with the screening currents of (textsf{SVir}). We also establish quadratic relations satisfied by (W_i(z)) and show that they generate a pair of commuting q-deformed Virasoro algebras, which degenerate into two nontrivial commuting Virasoro algebras included in (textsf{F} oplus textsf{SVir}).

A geometric framework, called multicontact geometry, has recently been developed to study action-dependent field theories. In this work, we use this framework to analyze symmetries in action-dependent Lagrangian and Hamiltonian field theories, as well as their associated dissipation laws. Specifically, we establish the definitions of conserved and dissipated quantities, define the general symmetries of the field equations and the geometric structure, and examine their properties. The latter ones, referred to as Noether symmetries, lead to the formulation of a version of Noether’s Theorem in this setting, which associates each of these symmetries with the corresponding dissipated quantity and the resulting conservation law.

Within the framework of the Riemann–Hilbert problem, the theory of inverse scattering transform is established for the defocusing nonlinear Schrödinger equation with local and nonlocal nonlinearities (which originates from the parity-symmetric reduction of the Manakov system) under nonzero boundary conditions. First, the adjoint Lax pair and auxiliary eigenfunctions are introduced for the direct scattering, and the analyticity, symmetries of eigenfunctions and scattering matrix are studied in detail. Then, the distribution of discrete eigenvalues is examined, and the asymptotic behaviors of the eigenfunctions and scattering coefficients are analyzed rigorously. Compared with the Manakov system, the reverse-space nonlocality introduces an additional symmetry, leading to stricter constraints on eigenfunctions, scattering coefficients and norming constants. Further, the Riemann–Hilbert problem is formulated for the inverse problem with the scattering coefficients admitting an arbitrary number of simple zeros. For the reflectionless case, the N-soliton solutions are presented in the determinant form. With N = 1, the dark and beating one-soliton solutions are obtained, which are, respectively, associated with a pair of discrete eigenvalues lying on and off the circle on the spectrum plane. Via the asymptotic analysis, the two-soliton solutions are found to admit the interactions between two dark solitons or two beating solitons, as well as the superpositions of two beating solitons or one beating soliton and one dark soliton.