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In this work, we study the nature of transitions between inherent structures of a two-dimensional model supercooled liquid. We demonstrate that these transitions occur predominately along a small number of directions on the energy…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
We study the stochastic thermodynamics of an overdamped harmonic chain, which can be viewed equivalently as a 1D Rouse chain or as an approximate model of single file diffusion. We discuss mainly two levels of description of this system:…
In this chapter we summarize recent developments in the study of kinetically constrained models (KCMs) as models for glass formers. After recalling the definition of the KCMs which we cover we study the possible occurrence of ergodicity…
We study the glass and jamming transition of finite-dimensional models of simple liquids: hard- spheres, harmonic spheres and more generally bounded pair potentials that modelize frictionless spheres in interaction. At finite temperature,…
We study a heteropolymer model with random contact interactions introduced some time ago as a simplified model for proteins. The model consists of self-avoiding walks on the simple cubic lattice, with contact interactions between nearest…
We study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via…
Thermodynamics controls structure, function, stability and morphology of polymer blends. However, obtaining the precise information about their mixing thermodynamics is a challenging task, especially when dealing with complex…
One of the key objectives in investigating small stochastic systems is the development of micrometer-sized engines and the understanding of their thermodynamics. However, the primary mathematical tool used for this purpose, the overdamped…
The thermal ratchets model toggles a spatially periodic asymmetric potential to rectify random walks and achieve transport of diffusing particles. We numerically solve the governing equation for the full dynamics of an infinite 1D ratchet…
Reconstructing a thermal model capable of efficiently simulating the behavior of a spacecraft from sparse and localized temperature measurements remains a challenging task. To address this, we introduce a physically-constrained calibration…
We describe a modified transfer matrix renormalization group (TMRG) algorithm and apply it to calculate thermodynamic properties of the one-dimensional t-J model. At the supersymmetric point we compare with Bethe ansatz results and make…
Dimensionality is a fundamental concept in physics, which plays a hidden but crucial role in various domains, including condensed matter physics, relativity and string theory, statistical physics, etc. In quantum physics, reducing…
The description of activated relaxation of glassy systems in the multidimensional configurational space is a long-standing open problem. We develop a phenomenological description of the out-of-equilibrium dynamics of a model with a rough…
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level…
It is common to study polymer physics through the use of idealized single-chain models, and the most popular of these is the freely jointed chain model. In certain thermodynamic ensembles, statistical mechanical treatment of this model is…
We explore a roughening phase transition that occurs in the entanglement dynamics of certain quantum circuits. Viewing entanglement as the free energy of a membrane in a circuit-defined random environment, there is a competition between…
We use computer simulations to study the thermodynamic properties of a glass former in which a fraction $c$ of the particles has been permanently frozen. By thermodynamic integration, we determine the Kauzmann, or ideal glass transition,…
A two-dimensional lattice gas model is proposed. The ground state of this model with a fixed density is neither periodic nor quasi-periodic. It also depends on system size in an irregular manner. On the other hand, it is ordered in the…
Dynamic facilitation theory assumes short-ranged dynamic constraints to be the essential feature of supercooled liquids and draws much of its conclusions from the study of kinetically constrained models. While deceptively simple, these…