Related papers: Dynamical Critical Exponent for Two-Species Totall…
We study the diffusion equation with an appropriate change of variables. This equation is in general a partial differential equation (PDE). With the self-similar and related Ansat\"atze we transform the PDE of diffusion to an ordinary…
The recently proposed exact quantum solution for two $\delta$-function-interacting particles with a mass-ratio $3\!:\!1$ in a hard-wall box [Y. Liu, F. Qi, Y. Zhang and S. Chen, iScience 22, 181 (2019)] violates the conventional necessary…
We consider a particle moving in one dimension, its velocity being a reversible diffusion process, with constant diffusion coefficient, of which the invariant measure behaves like $(1+|v|)^{-\beta}$ for some $\beta>0$. We prove that, under…
Quantum criticality of strongly attractive Fermi gas with $SU(3)$ symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The phase transitions driven by the chemical potential $\mu$, effective magnetic field…
We generalise Bray's self-consistent screening approximation to describe the critical dynamics of the $\phi^4$ theory. In order to obtain the dynamical exponent $z$, we have to make an ansatz for the form of the scaling functions, which…
Following the Bethe ansatz we determine the dynamical spectra of the one-dimensional supersymmetric t-J model. A series of fractionalized excitations are identified through two sets of Bethe numbers. Typical patterns in each set are found…
We consider a two-species chemotaxis model in $\R^d(d \ge 3)$ featuring nonlinear porous medium-type diffusion and nonlocal attractive power-law interaction. Here, the nonlinear diffusion is chosen to be $1/m_1+1/m_2=(d+2)/d$ in such a way…
Assume that $N_m(x)$ denotes the density of the population at a point $x$ at the beginning of the reproductive season in the $m$th year. We study the following impulsive reaction-diffusion model for any $m\in \mathbb Z^+$…
Using the analytic Bethe ansatz, we initiate a study of the scaling limit of the quasi-periodic $D^{(2)}_3$ spin chain. Supported by a detailed symmetry analysis, we determine the effective scaling dimensions of a large class of states in…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…
It is shown that the critical properties of a recently studied model for non-equilibrium wetting are robust if one extends the dynamic rules by single-particle diffusion on terraces of the wetting layer. Examining the behavior at the…
We consider an inhomogeneous quantum phase transition across a multicritical point of the XY quantum spin chain. This is an example of a Lifshitz transition with a dynamical exponent z = 2. Just like in the case z = 1 considered in New J.…
The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement $\langle X^2(t) \rangle = 2 D t^\alpha$. Motivated by experiments reporting populations of the anomalous diffusion parameters $\alpha$…
A quantitatively reliable theoretical description of the dynamics of fluctuations in non-equilibrium is indispensable in the experimental search for the QCD critical point by means of ultra-relativistic heavy-ion collisions. In this work we…
For a competition-diffusion blow-up system involving the fractional Laplacian of the form \begin{equation*}\label{syst1} -(-\Delta)^su=uv^2,\quad-(-\Delta)^sv=vu^2,\quad u,v>0 \ \mathrm{in} \ \mathbb{R}^N, \end{equation*} whith $s\in(0,1)$,…
Recently, the XXX spin chain with arbitrary boundary fields was successfully solved [1] via the off-diagonal Bethe ansatz method [2]. The correctness and the completeness of this solution were numerically verified by Nepomechie for one…
Two dimensional condensed matter is realised in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic…
The position $x(t)$ of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray $x=v_0 t$, where $v_0$ is the average drift. However,…
We study the critical behavior for inhomogeneous versions of the Curie-Weiss model, where the coupling constant $J_{ij}(\beta)$ for the edge $ij$ on the complete graph is given by $J_{ij}(\beta)=\beta w_iw_j/(\sum_{k\in[N]}w_k)$. We call…
We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with reflection) predict only two fold degeneracies.…