Related papers: Inhomogeneous states in two dimensional linear sig…
In this work we prove the nonlinear instability of inhomogeneous steady states solutions to the Hamiltonian Mean Field (HMF) model. We first study the linear instability of this model under a simple criterion by adapting the techniques…
Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are…
We consider the large-time behavior of sign-changing solutions of the inhomogeneous equation $u_t-\Delta u=|x|^\alpha |u|^{p}+\zeta(t)\,{\mathbf w}(x)$ in $(0,\infty)\times\mathbb{R}^N$, where $N\geq 3$, $p>1$, $\alpha>-2$, $\z, {\mathbf…
The thermodynamics of the O(N) linear and nonlinear sigma models in 3+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, temperature-independent renormalization is…
We discuss the two-dimensional Grassmannian $SU(N)/S(U(N-2)\times U(2))$ and the flag $SU(N)/S(U(N-2)\times U(1)\times U(1))$ sigma models on a finite interval and construct analytical solutions of gap equations in the large N limit. We…
The relation between collective modes and the phase transition in low density nuclear matter is examined. The dispersion relations for collective modes in a linear approach are evaluated within a Landau-Fermi liquid scheme by assuming…
An approximate equation for the effective conductivity sigma_eff of systems with a finite maximal scale of inhomogeneities is deduced. An exact solution of this equation is found and its physical meaning is discussed. A two-phase randomly…
In this paper we present a class of exact inhomogeneous solutions to Einstein's equations for higher dimensional Szekeres metric with perfect fluid and a cosmological constant. We also show particular solutions depending on the choices of…
We investigate various scenarios which include interaction forms between dark matter and dark energy that exhibit sign reverse, namely where the transfer of energy between the dark fluids changes sign during evolution. We study the…
A recently proposed approximate large-n ground state solution of the U_L(n)xU_R(n) symmetric linear sigma model is investigated at finite temperature. We study the coupled evaporation of two condensates corresponding to the symmetry…
Superconductors with low superfluid density can be described by XY models. In such models the scale of the transition temperature T_c is largely set by the zero temperature phase stiffness (helicity modulus), a long-wavelength property of…
In simulations of the 2D Ising model, we examine heterogeneous nucleation induced by a small impurity consisting of a line of $l$ fixed spins. As $l$ increases, we identify a limit of stability beyond which the metastable phase is not…
The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale…
We study O(N) symmetric supersymmetric models in three dimensions at finite temperature. These models are known to have an interesting phase structures. In particular, in the limit $N \to \infty$ one finds spontaneous breaking of scale…
We study here the equation of state of symmetric nuclear matter at finite temperatures using a modified SU(2) Chiral Sigma model. The effect of temperature on effective mass, pressure, entropy and binding energy is discussed. The liquid-gas…
We derive a finite set of nonlinear integral equations for describing the finite size dependence of the ground state energy of the O(4) nonlinear sigma model. By modifying the kernel functions of these equations we propose nonlinear…
We analyze long-time behavior of solutions to a class of problems related to very fast and singular diffusion porous medium equations having nonhomogeneous in space and time source terms with zero mean. In dimensions two and three, we…
We consider the nonlinear heat equation $u_t - \Delta u = |u|^\alpha u$ on ${\mathbb R}^N$, where $\alpha >0$ and $N\ge 1$. We prove that in the range $0 < \alpha <\frac {4} {N-2}$, for every $\mu >0$, there exist infinitely many…
We study a thermodynamically consistent model describing phenomena in a visco-plastic metal subjected to temperature changes. We complete the model with the mixed boundary condition on displacement and stress and Neumann-type condition for…
We study phase transition of a nonequilibrium statistical-mechanical model, in which two degrees of freedom with different time scales separated from each other touch to their own heat bath. A general condition for finding anomalous…