Related papers: On the KMS states for the Bernoulli shift
Suppose $\alpha$ is a rotationally symmetric norm on $L^{\infty}\left(\mathbb{T}\right) $ and $\beta$ is a "nice" norm on $L^{\infty}\left(\Omega,\mu \right) $ where $\mu$ is a $\sigma$-finite measure on $\Omega$. We prove a version of…
The two-dimensional one-component logarithmic Coulomb gas is mapped onto a non-hermitian fermionic field theory. At $\beta=2$, the field theory is free. Correlation functions are calculated and a perturbation theory is discussed for…
We prove a Weiss conjecture on $\beta$-admissibility of control and observation operators for discrete and continuous $\gamma$-hypercontractive semigroups of operators, by representing them in terms of shifts on weighted Bergman spaces and…
Consider the complete graph on $n$ vertices. To each vertex assign an Ising spin that can take the values $-1$ or $+1$. Each spin $i \in [n]=\{1,2,\dots, n\}$ interacts with a magnetic field $h \in [0,\infty)$, while each pair of spins $i,j…
We present new sharper lower and upper bounds for the non-zero Bernoulli numbers using Euler's formula for the Riemann zeta function. In particular, we determine the best possible constants $ \alpha $ and $ \beta $ such that the double…
Based on renormalization group arguments we establish that for a superconductor in the presence of a weak external magnetic field, $B$, the dependence on $B$ and the deviation from the critical temperature, $\tau$, of a thermodynamic…
If $\mu$ is a distribution over the $d$-dimensional Boolean cube $\{0,1\}^d$, our goal is to estimate its mean $p\in[0,1]^d$ based on $n$ iid draws from $\mu$. Specifically, we consider the empirical mean estimator $\hat p_n$ and study the…
We investigate the asymptotic behavior as $\varepsilon \to 0$ of singularly perturbed phase transition models of order $n \geq 2$, given by \begin{align} G_\varepsilon^{\lambda,n}[u] := \int_I \frac 1\varepsilon W(u)…
We define and study the properties of the infinite dimensional quantized Kronecker flow. This $\bC^*$-dynamical system arises as a quantization of the corresponding flow on an infinite dimensional torus. We prove an ergodic theorem for a…
We study a rotating atomic Fermi gas near a narrow s-wave Feshbach resonance in a uniaxial harmonic trap with frequencies $\Omega_\perp$, $\Omega_z$. Our primary prediction is the upper-critical angular velocity, $\omega_{c2} (\delta,T)$,…
We consider ontological models of a quantum system, assuming that not all probability distributions over the space $\Lambda$ of ontic states are preparable, only those belonging to a certain set C. We assume further that every POVM with a…
The Coulomb gap in a donor-acceptor model with finite charge transfer energy $\Delta$ describing the electronic system on the dielectric side of the metal-insulator transition is investigated by means of computer simulations on two- and…
For sequences $\alpha \equiv \{\alpha_n\}_{n=0}^{\infty}$ of positive real numbers, called weights, we study the weighted shift operators $W_{\alpha}$ having the property of moment infinite divisibility ($\mathcal{MID}$); that is, for any…
We investigate the quantum dynamics of a quantum oscillator coupled with the most upper state of a three-level $\Lambda-$ type system. The two transitions of the three-level emitter, possessing orthogonal dipole moments, are coherently…
Katok conjectured that every $C^{2}$ diffeomorphism $f$ on a Riemannian manifold has the intermediate entropy property, that is, for any constant $c \in[0, h_{top}(f))$, there exists an ergodic measure $\mu$ of $f$ satisfying…
Consider a cellular automaton with state space $\{0,1 \}^{{\mathbb Z}^2}$ where the initial configuration $\omega_0$ is chosen according to a Bernoulli product measure, 1's are stable, and 0's become 1's if they are surrounded by at least…
In this short paper, the commutator of monomials of operators obeying constant commutation relations is expressed in terms of anticommutators. The formula involves Bernoulli numbers or Euler polynomials evaluated in zero. The role of…
The parabolic problem $u_t-\Delta u=\frac{\lambda f(x)}{(1-u)^2}+P$ on a bounded domain $\Omega$ of $R^n$ with Dirichlet boundary condition models the microelectromechanical systems(MEMS) device with an external pressure term. In this…
We study the $N$-dependent behaviour of $\mathrm{2d}$ causal set quantum gravity. This theory is known to exhibit a phase transition as the analytic continuation parameter $\beta$, akin to an inverse temperature, is varied. Using a scaling…
As pointed out by Coleman, physical quantities in the Schwinger model depend on a parameter $\theta$ that determines the background electric field. There is a phase transition for $\theta = \pi$ only. We develop a momentum space formalism…