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The grand partition function of a model of confined quarks is exactly calculated at arbitrary temperatures and quark chemical potentials. The model is inspired by a softly BRST-broken version of QCD and possesses a quark mass function…
We study the thermodynamics of the relativistic quantum O($N$) model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form…
We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of…
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…
In this Letter, we analyze the quantum dynamics of the perceptron model: a particle is constrained on a $N$-dimensional sphere, with $N\to \infty$, and subjected to a set of randomly placed hard-wall potentials. This model has several…
A unified (classical-quantum-statistical) formalism for a system with continuous spectrum is introduced. For this kind of systems ergodicity behavior and the existence of microcanonical and canonical (KMS) equilibrium is proved. It is…
Unboundedness of solutions is shown to occur in a one-dimensional quasilinear parabolicparabolic chemotaxis system for any initial mass. Our result is also independent of the relation between the speeds of the diffusion of cells and…
This paper is concerned with a chemotaxis aggregation model for cells, more precisely with a parabolic-elliptic semilinear Patlak-Keller-Segel system in a ball of $\mathbb{R}^N$ for $N\geq 2$. For $N=2$, this system is well known for its…
The first law of thermodynamics imposes not just a constraint on the energy-content of systems in extreme quantum regimes, but also symmetry-constraints related to the thermodynamic processing of quantum coherence. We show that this…
The theory of deconfined quantum critical points describes phase transitions at temperature T = 0 outside the standard paradigm, predicting continuous transformations between certain ordered states where conventional theory requires…
The thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, only the minimum of the effective potential can be…
The basic elements of the mathematical theory of states of thermal equilibrium of infinite systems of quantum anharmonic oscillators (quantum crystals) are outlined. The main concept of this theory is to describe the states of finite…
Near a quantum critical point (QCP) in a metal, strong Fermion-Fermion interactions mediated by soft collective bosons give rise to two competing phenomena: non-Fermi liquid behavior and superconductivity that deviates from conventional BCS…
We study a system of two coupled nonlinear parabolic equations. It constitutes a variant of the Keller-Segel model for chemotaxis, i.e. it models the behaviour of a population of bacteria that interact by means of a signalling substance. We…
In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter $K_c$. We obtain the asymptotic…
We consider a nonrelativistic cosmological model introduced in [1] and derived as the nonrelativistic limit (or approximation at sub-Hubble scales) of a general relativistic model in [3, 4]. The latter is defined by an energy-momentum…
We study the hydrodynamic limit for some conservative particle systems with degenerate rates, namely with nearest neighbor exchange rates which vanish for certain configurations. These models belong to the class of {\sl kinetically…
The quantum O(N) model in the infinite $N$ limit is a paradigm for symmetry-breaking. Qualitatively, its phase diagram is an excellent guide to the equilibrium physics for more realistic values of $N$ in varying spatial dimensions ($d>1$).…
We analyze in detail, beyond the usual scaling hypothesis, the finite-size convergence of static quantities toward the thermodynamic limit. In this way we are able to obtain sequences of pseudo-critical points which display a faster…
The equilibrium thermodynamic properties of the SU(N) plasma at finite temperature are studied non-perturbatively in the large-N limit, via lattice simulations. We present high-precision numerical results for the pressure, trace of the…