178 citations · 981 across the 75 of their papers we have counts for
48 papers · 1 filter
On light cone bounds for Markov quantum open systems
Israel Michael Sigal, Xiaoxu Wu
We study space-time behaviour of solutions of the von Neumann-Lindblad equations underlying the dynamics of Markov quantum open systems. For a large class of these equations, we pr…
Macroscopic suppression of supersonic quantum transport
Jérémy Faupin, Marius Lemm, Israel Michael Sigal +1
We consider a broad class of strongly interacting quantum lattice gases, including the Fermi-Hubbard and Bose-Hubbard models. We focus on macroscopic particle clusters of size …
Information propagation in long-range quantum many-body systems
Marius Lemm, Carla Rubiliani, Israel Michael Sigal +1
We study general lattice bosons with long-range hopping and long-range interactions decaying as with . We find a linear light cone for the informatio…
On propagation of information in quantum many-body systems
Israel Michael Sigal, Jingxuan Zhang
We prove bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general lattice quantum many-body systems. The proofs are…
Instability of electroweak homogeneous vacua in strong magnetic fields
Adam Gardner, Israel Michael Sigal
We consider the classical vacua of the Weinberg-Salam (WS) model of electroweak forces. These are no-particle, static solutions to the WS equations minimizing the WS energy locally…
Differential Equations of Quantum Mechanics
Israel Michael Sigal
We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems.
On Lieb-Robinson bounds for the Bose-Hubbard model
Jérémy Faupin, Marius Lemm, Israel Michael Sigal
We consider the dynamics of the Bose-Hubbard model on general lattices and prove a Lieb-Robinson bound for observables whose supports are separated by an initially almost particle-…
The Feshbach-Schur map and perturbation theory
Geneviève Dusson, Israel Sigal, Benjamin Stamm
This paper deals with perturbation theory for discrete spectra of linear operators. To simplify exposition we consider here self-adjoint operators. This theory is based on the Fesh…
Vortex Lattices and the Bogoliubov-De Gennes Equations
Ilias, Chenn, Israel Michael Sigal
We consider the Bogoliubov-de Gennes equations giving an equivalent formulation of the BCS theory of superconductivity. We are interested in static solutions with the magnetic fiel…
On Derivation of the Poisson-Boltzmann Equation
Ilias, Chenn, Israel Michael Sigal
Starting from the microscopic reduced Hartree-Fock equation, we derive the nanoscopic linearized Poisson-Boltzmann equation for the electrostatic potential associated with the elec…
Maximal Speed of Quantum Propagation
Jack Arbunich, Fabio Pusateri, Israel Michael Sigal +1
For Schroedinger equations with both time-independent and time-dependent Kato potentials, we give a simple proof of the maximal speed bound. The latter states that the probability…
Vortex lattice solutions of the ZHK Chern-Simons equations
Krishan Rajaratnam, Israel Michael Sigal
We consider the non-relativistic Chern-Simons equations proposed by Zhang, Hansen and Kivelson as the mean field theory of the fractional Hall effect. We prove the existence of the…
On the Hartree-Fock-Bogoliubov equations
Volker Bach, Sébastien Breteaux, Thomas Chen +2
We review some results of our paper arXiv:1602.05171v2 on the "nonlinear quasifree approximation" to the many-body Schrödinger dynamics of Bose gases. In that paper, we derive, wit…
On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations
Li Chen, Panayotis Smyrnelis, Israel Michael Sigal
We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations of superconductivity, with multiple magnetic flux quanta per a fundamental cell. We also r…
On the Bogolubov-de Gennes Equations
Ilias, Chenn, Israel Michael Sigal
We consider the Bogolubov-de Gennes equations giving an equivalent formulation of the BCS theory of superconductivity. We are interested in the case when the magnetic field is pres…
The time-dependent Hartree-Fock-Bogoliubov equations for Bosons
Volker Bach, Sébastien Breteaux, Thomas Chen +2
In this article, we use quasifree reduction to derive the time-dependent Hartree-Fock-Bogoliubov (HFB) equations describing the dynamics of quantum fluctuations around a Bose-Einst…
Magnetic Vortices, Abrikosov Lattices and Automorphic Functions
Israel Michael Sigal
We address the macroscopic theory of superconductivity - the Ginzburg-Landau theory. This theory %Macroscopic theory of superconductivity is based on the celebrated Ginzburg - Land…
On stability of Abrikosov vortex lattices
Israel Michael Sigal, Tim Tzaneteas
The Ginzburg-Landau equations play a key role in superconductivity and particle physics. They inspired many imitations in other areas of physics. These equations have two remarkabl…
Hamiltonian dynamics of a particle interacting with a wave field
Daniel Egli, Jürg Fröhlich, Zhou Gang +2
We study the Hamiltonian equations of motion of a heavy tracer particle interacting with a dense weakly interacting Bose-Einstein condensate in the classical (mean-field) limit. So…
On Rayleigh scattering in non-relativistic quantum electrodynamics
Jeremy Faupin, Israel Michael Sigal
In this note we provide details of the proofs of the main results of our paper [19] to the standard model of non-relativistic quantum electrodynamics in which particles are minimal…
Comment on the photon number bound and Rayleigh scattering
Jeremy Faupin, Israel Michael Sigal
We discuss photon number bounds for a system of non-relativistic particles coupled to the quantized electromagnetic field (non-relativistic QED), below the ionization threshold. Su…
Long Range Behaviour of van der Waals Force
Ioannis Anapolitanos, Israel Michael Sigal
We prove van der Waals - London's law of decay of the van der Waals force for a collection of neutral atoms at large separation.
On quantum Huygens principle and Rayleigh scattering
Jeremy Faupin, Israel Michael Sigal
We prove several minimal photon velocity estimates below the ionization threshold for a particle system coupled to the quantized electromagnetic or phonon field. Using some of thes…
Effective dynamics of an electron coupled to an external potential in non-relativistic QED
Volker Bach, Thomas Chen, Jeremy Faupin +2
In the framework of non-relativistic QED, we show that the renormalized mass of the electron (after having taken into account radiative corrections) appears as the kinematic mass i…