相关论文: Quantum Integrability of Certain Boundary Conditio…

The deformed supersymmetric sine-Gordon model, obtained through known deformation of the corresponding potential, is found to be quasi-integrable, like its non-supersymmetric counterpart, which was observed earlier. The system expectedly…

We study a three dimensional conformal field theory in terms of its partition function on arbitrary curved spaces. The large $N$ limit of the nonlinear sigma model at the non-trivial fixed point is shown to be an example of a conformal…

In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $\nu$, of diffusive type. In particular, we assume $\nu$ is symmetric and…

We consider the Hamiltonian system with Neumann boundary conditions: \[ -\Delta u + \mu u=v^{q }, \quad -\Delta v+ \mu v=u^{p} \quad \text{ in $\Omega$}, \qquad u, v >0 \quad \text{ in $\Omega$,} \qquad \partial_\nu u= \partial_\nu v=0…

Non-perturbative renormalization group approach suggests that a large class of nonlinear sigma models are renormalizable in three dimensional space-time, while they are non-renormalizable in perturbation theory. ${\cal N}=2$ supersymmetric…

To analyse pure ${\cal N}=2$ $SU(2)$ gauge theory in the Nekrasov-Shatashvili (NS) limit (or deformed Seiberg-Witten (SW)), we use the Ordinary Differential Equation/Integrable Model (ODE/IM) correspondence, and in particular its (broken)…

We present the so-called Liouville-Neumann (LN) approach to nonequilibrium quantum fields. The LN approach unifies the functional Schr\"{o}dinger equation and the LN equation for time-independent or time-dependent quantum systems and for…

In this paper we define a new class of the quantum integrable systems associated with the quantization of the cotangent bundle $T^*(GL(N))$ to the Lie algebra $\frak{gl}_N$. The construction is based on the Gelfand-Zetlin maximal commuting…

The non-commutative O(N) Gross-Neveu model is solved in the large N limit in two and three space-time dimensions. The commutative version of the two dimensional model is a renormalizable quantum field theory, both in a coupling constant…

In this paper we study the Klein-Gordon (KG) lattice with periodic boundary conditions. It is an $N$ degrees of freedom Hamiltonian system with linear inter-site forces and nonlinear on-site potential, which here is taken to be of the…

Starting from the Bethe Ansatz solution of the open integrable spin-1 XXZ quantum spin chain with diagonal boundary terms, we derive a set of nonlinear integral equations (NLIEs), which we propose to describe the boundary supersymmetric…

We consider in this paper the nonlinear elliptic equation with Neumann boundary condition \begin{align*} \begin{cases} \Delta u=a|u|^{m-1}u\,\,\mbox{ in }\,\,\rnp\\ \dfrac{\partial u}{\partial t}=b|u|^{\eta-1}u+f\,\,\mbox{ on…

We construct an action for the N=2 supersymmetric sine-Gordon model on the half-line, which we argue is both supersymmetric and integrable. The boundary interaction depends on three continuous boundary parameters, as well as the bulk mass…

We canonically quantize $O(D+2)$ nonlinear sigma models (NLSMs) with theta term on arbitrary smooth, closed, connected, oriented $D$-dimensional spatial manifolds $\mathcal{M}$, with the goal of proving the suitability of these models for…

We study large $N$ limits of the hyperbolic $O(N)$ linear sigma model ($\text{HLSM}_N$) on the two-dimensional torus $\mathbb T^2$, namely, a system of $N$ interacting stochastic damped nonlinear wave equations (SdNLW) with coupled cubic…

We present three groups of examples of Wigner Quantum Systems related to the Lie superalgebras $osp(1/6n)$, $sl(1/3n)$ and $sl(n/3)$ and discuss shortly their physical features. In the case of $sl(1/3n)$ we indicate that the underlying…

The quantum O(N) model in the infinite $N$ limit is a paradigm for symmetry-breaking. Qualitatively, its phase diagram is an excellent guide to the equilibrium physics for more realistic values of $N$ in varying spatial dimensions ($d>1$).…

Aiming at studying the emergence of Non-Equilibrium Steady States (NESS) in quantum integrable models by means of an exact analytical method, we focus on the Tonks-Girardeau or hard-core boson limit of the Lieb-Liniger model. We consider…

The hierarchy of equations belonging to two different but related integrable systems, the Nonlinear Schr\"odinger and its derivative variant, DNLS are subjected to two distinct deformation procedures, viz. quasi-integrable deformation (QID)…

This work deals with the system $(-\Delta)^m u= a(x) v^p$, $(-\Delta)^m v=b(x) u^q$ with Dirichlet boundary condition in a domain $\Omega\subset\RR^n$, where $\Omega$ is a ball if $n\ge 3$ or a smooth perturbation of a ball when $n=2$. We…