Statistical Mechanics
We identify a new universality class of phase transitions that emerges in non-normal systems, extending the classical framework beyond eigenvalue instabilities. Unlike traditional critical phenomena, where transitions occur when eigenvalues…
Driven critical dynamics in quantum phase transitions holds significant theoretical importance, and also practical applications in fast-developing quantum devices. While scaling corrections have been shown to play important roles in fully…
We review the field-theoretic renormalization-group approach to critical properties of flat polymerized membranes. We start with a presentation of the flexural effective model that is entirely expressed in terms of a transverse (flexural)…
We study the effect of spatially-varying potential and diffusivity on the dispersion of a tracer particle in single-file diffusion. Non-interacting particles in such a system exhibit normal diffusion at late times, which is characterised by…
Mixed states can exhibit two distinct kinds of symmetries, either on the level of the individual states (strong symmetry), or only on the level of the ensemble (weak symmetry). Strong symmetries can be spontaneously broken down to weak…
We solve exactly the non-equilibrium dynamics of two discrete random walkers moving in channels with transition rates $p \neq q$ that swap positions at a rate $s$. We compute exactly the joint probability distribution $P_{n,m}(t)$ for the…
Controlling dopant transport with high spatial precision is crucial for improving the semiconductor functionality, reliability, and scalability. Although prior models of noise-assisted diffusion have been largely confined to idealized one…
We propose a variational framework for nonequilibrium thermodynamics built around the effective number of accessible state, a multiplicative count that ranges from for a uniform distribution to one under complete localization, and whose…
The mean back relaxation (MBR) relates the value of a stochastic process at three different time points. It has been shown to detect broken detailed balance under certain conditions. For experiments of probe particles in living and…
We study the directed transport of bosons along a one dimensional lattice in a dissipative setting, where the hopping is only facilitated by coupling to a Markovian reservoir. By combining numerical simulations with a field-theoretic…
We consider a one-dimensional run-and-tumble particle (RTP) confined by an external potential and coupled to a thermal reservoir. Starting from the corresponding Fokker-Planck equation, we derive an explicit expression for the local entropy…
We investigate the spin-$1$ Blume-Capel model on an infinite strip of the triangular lattice using the transfer-matrix method combined with a sparse-matrix factorization technique. Through finite-size scaling analysis of numerically exact…
We study Yang-Lee zeros in the thermodynamic limit of the 2D nearest-neighbor antiferromagnetic Ising model on square and triangular lattices. We employ the Numerical Linked Cluster Expansion (NLCE) equipped with Exact Enumeration (EE) of…
Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective…
Fluctuating pairwise interactions are understood to drive fluid-like states in dense biological systems. These states find a broad range of functionalities, such as directing growth during morphogenesis and forming aggregates with…
The transition to an absorbing phase in a spatiotemporal system is a well-investigated nonequilibrium dynamic transition. The absorbing phase transitions fall into a few universality classes, defined by the critical exponents observed at…
Symmetry breaking underlies diverse phenomena from phase transitions in condensed matter to fundamental interactions in gauge theories. Despite many proposed indicators, a general quantification of symmetry breaking that is faithful,…
First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or…
We analyze underdamped Brownian motion in non-isothermal media with quadratic, linear, and piecewise-constant temperature profiles. Exact identities for entropy production and entropy extraction are derived, addressing whether a vanishing…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…