相关论文: On Matrix Product Ground States for Reaction-Diffu…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
We use the matrix product formalism to find exact ground states of two new spin-1 quantum chains with nearest neighbor interactions. One of the models, model I, describes a one-parameter family of quantum chains for which the ground state…
We introduce a class of $n$-dimensional (possibly inhomogeneous) spin-like lattice systems presenting modulated phases with possibly different textures. Such systems can be parameterized according to the number of ground states, and can be…
A complete classification is given for one dimensional chains with nearest neighbor interactions having two states in each site, for which a matrix product ground state exists. The Hamiltonians and their corresponding matrix product ground…
Matrix product ansatz (MPA) is a powerful framework for constructing exact steady state weights of one dimensional non-equilibrium stochastic processes; but its generalization to higher dimensions is limited. Here, we introduce the MPA…
We introduce and solve a model of hardcore particles on a one dimensional periodic lattice which undergoes an active-absorbing state phase transition at finite density. In this model an occupied site is defined to be active if its left…
A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble,…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
Input-output, growth-decay, production-consumption type situations abound in many practical problems. When the input and output variables are independently gamma distributed, various aspects of the residual effect are already tackled by the…
We consider a generalized coagulation-decoagulation system on a one-dimensional discrete lattice with reflecting boundaries. It is known that a Bernoulli shock measure with two shock fronts might have a simple random-walk dynamics, provided…
We find the exact solution for the stationary state measure of the partially asymmetric exclusion process on a ring with multiple species of particles. The solution is in the form of a matrix product representation where the matrices for a…
Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of non-equilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the…
For an interacting spatio-temporal lattice system we introduce a formal way of expressing multi-time correlation functions of local observables located at the same spatial point with a time state, i.e. a statistical distribution of…
We have developed a new approach based on matrix product representations of ground states to study Quantum Phase Transitions (QPT). As confirmation of the power of our approach we have analytically analyzed the XXZ spin-one chain with…
We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix…
Recently it has been shown that the zero-energy eigenstate -- corresponding to the stationary state -- of a stochastic Hamiltonian with nearest-neighbour interaction in the bulk and single-site boundary terms, can always be written in the…
We study the effects due to limited entanglement in the one-dimensional Hubbard model by representing the ground states in the form of the matrix product states. Finite-entanglement scaling behavior over a wide range is observed at…
It is shown that the simplest multiplicative random complex matrix model generalizes the large-N phase structure found in the unitary case: A perturbative regime is joined to a nonperturbative regime at a point of nonanalyticity.
Posttranslational modification of proteins is key in transmission of signals in cells. Many signaling pathways contain several layers of modification cycles that mediate and change the signal through the pathway. Here, we study a simple…
A generalization of matrix product states (MPS) is introduced which is suitable for describing interacting quantum systems in two and three dimensions. These scale-renormalized matrix-product states (SR-MPS) are based on a course-graining…