Related papers: The Lieb-Thirring inequality for interacting syste…
We derive a Pauli exclusion principle for extended fermion-based anyons of any positive radius and any non-trivial statistics parameter. That is, we consider 2D fermionic particles coupled to magnetic flux tubes of non-zero radius, and…
We consider the quantum evolution of a pair of interacting atoms in a three dimensional isotropic trap where the interaction strength is quenched from one value to another. Using exact solutions of the static problem we are able to evaluate…
Combining the methods of Cuenin [2019] and Borichev-Golinskii-Kupin [2009, 2018], we obtain the so-called Lieb-Thirring inequalities for non-selfadjoint perturbations of an effective Hamiltonian for bilayer graphene.
We investigate the entanglement structure of a bipartite quantum system through the lens of quantum thermodynamics in the absence of conformal symmetry. Specifically, we consider the long-range Kitaev model, where the pairing interaction…
We study the quantum dynamics of a single mode/particle interacting inhomogeneously with a large number of particles and introduce an effective approach to find the accessible Hilbert space where the dynamics takes place. Two relevant…
The finite-rank Lieb-Thirring inequality provides an estimate on a Riesz sum of the $N$ lowest eigenvalues of a Schr\"odinger operator $-\Delta-V(x)$ in terms of an $L^p(\mathbb{R}^d)$ norm of the potential $V$. We prove here the existence…
We consider ground states of a pseudo-relativistic Fermi system in the $L^2$-critical case. We prove that the system admits ground states, if and only if the attractive strength $a$ satisfies $0<a<D_{4/3,2}$, where $D_{4/3,2}\in(0, \infty)$…
We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi operators, which are nearly as strong as those proven previously for the case of selfadjoint operators by Hundertmark and Simon. We use a method based on…
We apply wave packet methods to study an ion-trap system in the strong excitation regime imposing neither the rotating wave nor the Lamb-Dicke approximations. By this approach we show the existence of states with restricted phase space…
We consider translation-invariant interacting particle systems on the lattice with finite local state space admitting at least one Gibbs measure as a time-stationary measure. The dynamics can be irreversible but should satisfy some mild…
We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance $d$. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle…
In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently…
We generalize to multi-commutators the usual Lieb-Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expansions) in order to estimate…
When particles interact via two-body short-range central potential wells, binding can occur for some critical values of the coupling constants. Using the envelope theory, upper bounds for critical coupling constants are computed for quantum…
We investigate the relaxation dynamics of the integrable Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The system is initially prepared in its…
We consider a scalar quantum field theory with global $O(N)^3$ symmetry in four Euclidean dimensions and solve it numerically in closed form in the large-N limit. For imaginary tetrahedral coupling the theory is asymptotically free, with…
We derive exact closed form expressions for the first few terms of the short-distance Taylor expansion of the one-body correlation function of the Lieb-Liniger gas. As an intermediate result we obtain the high-p asymptotics of the momentum…
We explore the fundamental limits on thermodynamic irreversibility when cooling a quantum system in the presence of a finite-size reservoir. First, we prove that for any non-interacting $n$-particle reservoir, the entropy production…
We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but involving an additional gradient correction. The result is…
The Lieb-Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low dimensional quantum systems. In this note, we present various methods for…