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We have been investigating the problem of the Anderson localization in a disordered one dimensional tight-binding model. The disorder is created by the interaction of mobile particles with other species, immobilized at random positions. We…
The thermodynamical properties of heterogeneous DNA sequences are computed by path integral techniques applied to a nonlinear model Hamiltonian. The base pairs relative displacements are interpreted as time dependent paths whose amplitudes…
Spreading processes are often modelled as a stochastic dynamics occurring on top of a given network with edge weights corresponding to the transmission probabilities. Knowledge of veracious transmission probabilities is essential for…
Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic method which allows to select the level of resolution at which a fluid is simulated. In this work, we study the consistency of the resulting thermodynamic properties as a…
We consider continuous and discrete (1+1)-dimensional wetting models which undergo a localization/delocalization phase transition. Using a simple approach based on Renewal Theory we determine the precise asymptotic behavior of the partition…
We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions, in the presence of translational diffusion. This series solution allows us to efficiently…
The 1D Ising model is the simplest Hamiltonian-based model in statistical mechanics. The sim- plest interacting particle process is the Symmetric Exclusion Process (SEP), a 1D lattice gas of particles that hop symmetrically and cannot…
We derive and validate a partition function for low-dimensional systems interacting with a heat bath, addressing the general issue of thermodynamic modeling of nanoscale systems. In contrast to bulk systems in the canonical (NVT) ensemble…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime (the first passage time) of a system. The statistical distributions that can be obtained out of the mesoscopic description…
We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic…
The low temperature thermodynamics of correlated 1D fermionic models with spin and charge degrees of freedom is obtained by exact diagonalization (ED) of small systems and followed by density matrix renormalization group (DMRG) calculations…
We have formulated a family of machine learning problems as the time evolution of Parametric Probabilistic Models (PPMs), inherently rendering a thermodynamic process. Our primary motivation is to leverage the rich toolbox of thermodynamics…
A quantum model on the chemically and physically induced pluripotency in stem cells is proposed. Based on the conformational Hamiltonian and the idea of slow variables (molecular torsions) slaving fast ones the conversion from the…
We consider linear systems subject to packet dropouts and obtain necessary and sufficient conditions for an arbitrary state transfer and state estimation over a finite time instance $T$. The data loss signal is modeled using the Bernoulli…
A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small…
We show how thermodynamic properties of molecular models can be computed over a large, multidimensional parameter space by combining multistate reweighting analysis with a linear basis function approach. This approach reduces the…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
Here we present a combinatorial decision problem, inspired by the celebrated quiz show called the countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic…
The new scheme employed (throughout the thermodynamic phase space), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions are formulated…
The solidification and macro-segregation problem involving unsteady multi-physics and multi-phase fields is typically a complex process with mass, momentum, heat, and species transfers among solid, mushy, and liquid phase regions. The…