Related papers: On Matrix Product Ground States for Reaction-Diffu…

In this note we discuss how the matrix product solution for the steady state of the harmonic process is obtained from the solutions already known in the literature, i.e. the closed-form expression derived in arXiv:2107.01720 and the nested…

We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…

We investigate the ground-state properties of the quasi-one-dimensional dipolar gases using continuous matrix product states techniques. Making use of the first- and second-order correlation functions, we find that the system supports the…

Stochastic fluid-fluid models (SFFMs) offer powerful modeling ability for a wide range of real-life systems of significance. The existing theoretical framework for this class of models is in terms of operator-analytic methods. For the first…

A useful concept for finding numerically the dominant correlations of a given ground state in an interacting quantum lattice system in an unbiased way is the correlation density matrix. For two disjoint, separated clusters, it is defined to…

We study a class of stochastic ballistic annihilation and coalescence models with a binary velocity distribution in one dimension. We obtain an exact solution for the density which reveals a universal phase diagram for the asymptotic…

A reaction--diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Properties of stationary solutions together with their…

A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…

The variety of uniform matrix product states arises both in algebraic geometry as a natural generalization of the Veronese variety, and in quantum many-body physics as a model for a translation-invariant system of sites placed on a ring.…

We present a matrix-product-state-based numerical approach for simulating systems composed of several qubits and a common one-dimensional waveguide. In the presented approach, the one-dimensional waveguide is modeled in real space. Thus,…

We consider a lattice-gas model with an infinite range pairwise noncovex interaction. It might be relevant, for example, for adsorption of alkaline elements on W(112) and Mo(112). We study a competition between the effective dipole-dipole…

The possibility of a matrix product representation for eigenstates with energy and momentum zero of a general m-state quantum spin Hamiltonian with nearest neighbour interaction and periodic boundary condition is considered. The quadratic…

Using the matrix product ansatz, we obtain solutions of the steady-state distribution of the two-species open one-dimensional zero range process. Our solution is based on a conventionally employed constraint on the hop rates, which…

We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where…

A one dimensional XX spin chain of finite length coupled to reservoirs at both ends is solved exactly in terms of a matrix product state ansatz. An explicit representation of matrices of fixed dimension 4 independent of the chain length is…

We show the explicit expression of the geometric phase for $n$-partite Gaussian states. In our analysis, the covariance matrix can be obtained as a boundary term of the geometric phase.

We describe a simple method to find the ground state energy without calculating the expectation value of the Hamiltonian in the time-evolving block decimation algorithm with tensor network states. For example, we consider quantum…

The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low energy initial…

We study one- and two-dimensional models which undergo a transition between active and absorbing phases. The transition point in these models is of novel type: jump of the order parameter coincides with its power-law singularity. Some…

Mechanically induced crystallographic phase transformation that reflects dynamic stress responses of intrinsically stochastic nature is a pertinent yet much less well-understood phenomenon. We focus on understanding the physical…