Related papers: On the KMS states for the Bernoulli shift
We study the quantum critical behavior in an isotropic Fermi liquid in the vicinity of a zero-temperature density-wave transition at a finite wave vector q_c. We show that, near the transition, the Landau damping of the soft bosonic mode…
We consider the general supersymmetric one-dimensional quantum system with boundary, critical in the bulk but not at the boundary. The renormalization group flow on the space of boundary conditions is generated by the boundary beta…
Strange metals appear in a wide range of correlated materials. Electronic localization-delocalization and the expected loss of quasiparticles characterize beyond-Landau metallic quantum critical points and the associated strange metals.…
We present a detailed study of the properties of the phase transition in the four-dimensional compact U(1) lattice gauge theory supplemented by a monopole term, for values of the monopole coupling $\lambda$ such that the transition is of…
An integer matrix $A\in M_d(\Z)$ induces a covering $\sigma_A$ of $\T^d$ and an endomorphism $\alpha_A:f\mapsto f\circ \sigma_A$ of $C(\T^d)$ for which there is a natural transfer operator $L$. In this paper, we compute the KMS states on…
Spielberg has recently shown that Baumslag-Solitar groups associated to pairs of positive integers are quasi-lattice ordered in the sense of Nica. Thus they have tractable Toeplitz algebras. Each of these algebras carries a natural…
We simulate 3-flavour lattice QCD at small isospin chemical potential $\mu_I$ and finite temperature $T$. At $\mu_I=0$ there is a critical mass $m_c$ where the finite-temperature transition changes from first order to a crossover. We…
We consider random iteration of exponential entire functions, i.e. of the form ${\mathbb C}\ni z\mapsto f_\lambda(z):=\lambda e^z\in\mathbb C$, $\lambda\in{\mathbb C}\setminus \{0\}$. Assuming that $\lambda$ is in a bounded closed interval…
We present a proof of the central limit theorem for a pair of mutually non-commuting operators in mixing quantum spin chains. The operators are not necessarily strictly local but quasi-local. As a corollary we obtain a direct construction…
Scalar BMS-invariant QFT defined on the causal boundary $\scri$ of an asymptotically flat spacetime is discussed. (a)(i) It is noticed that the natural $BMS$ invariant pure quasifree state $\lambda$ on $\cW(\scri)$, recently introduced by…
We study a one-dimensional singular potential plus three types of regular interactions: constant electric field, harmonic oscillator and infinite square well. We use the Lippman-Schwinger Green function technique in order to search for the…
The two-dimensional $q$-state clock model for $q \geq 5$ undergoes two Berezinskii-Kosterlitz-Thouless (BKT) phase transitions as temperature decreases. Here we report an extensive worm-type simulation of the square-lattice clock model for…
We consider a modified version of the one-dimensional Hubbard model, the t1-t2 Hubbard chain, which includes an additional next-nearest-neighbor hopping. It has been shown that at weak coupling this model has a Luttinger liquid phase or a…
We prove a quantitative stability result for the Brunn-Minkowski inequality: if $|A|=|B|=1$, $t \in [\tau,1-\tau]$ with $\tau>0$, and $|tA+(1-t)B|^{1/n}\leq 1+\delta$ for some small $\delta$, then, up to a translation, both $A$ and $B$ are…
We prove rigorously that the ferromagnetic Ising model on any nonamenable Cayley graph undergoes a continuous (second-order) phase transition in the sense that there is a unique Gibbs measure at the critical temperature. The proof of this…
Moments of moments of the Riemann zeta function, defined by \[ \text{MoM}_T (k,\beta) = \frac{1}{T} \int_T^{2T} \left( \int_{ |h|\leq (\log T)^\theta}|\zeta(\tfrac{1}{2} + i t + ih)|^{2\beta} dh \right)^k dt \] where $k,\beta \geq 0$ and…
We consider classical and quantum dynamics on potentials that are asymptotically unbounded from below. By explicit construction we find that quantum bound states can exist in certain bottomless potentials. The classical dynamics in these…
On a smooth bounded 2-dimensional domain $\Omega$ we study the heat flow $u_t=\Delta u +\lambda (t)ue^{u^2}$ ($\lambda(t)$ is such that $d/dt ||u(t,\cdot)||_{H^1_0}=0$) introduced by T. Lamm, F. Robert and M. Struwe to investigate the…
We study the statistics of the condition number $\kappa=\lambda_{\mathrm{max}}/\lambda_{\mathrm{min}}$ (the ratio between largest and smallest squared singular values) of $N\times M$ Gaussian random matrices. Using a Coulomb fluid…
For intermediate Coulomb energy to Fermi energy ratios $r_s$, spinless fermions in a two-dimensional random potential form a new quantum phase, different from the Fermi glass (weakly interacting Anderson localized states) and the Wigner…