62 research outputs found
Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow
We study surfaces evolving by mean curvature flow (MCF). For an open set of
initial data that are -close to round, but without assuming rotational
symmetry or positive mean curvature, we show that MCF solutions become singular
in finite time by forming neckpinches, and we obtain detailed asymptotics of
that singularity formation. Our results show in a precise way that MCF
solutions become asymptotically rotationally symmetric near a neckpinch
singularity.Comment: This revision corrects minor but potentially confusing misprints in
Section
Ionization of Atoms in a Thermal Field
We study the stationary states of a quantum mechanical system describing an
atom coupled to black-body radiation at positive temperature. The stationary
states of the non-interacting system are given by product states, where the
particle is in a bound state corresponding to an eigenvalue of the particle
Hamiltonian, and the field is in its equilibrium state. We show that if Fermi's
Golden Rule predicts that a stationary state disintegrates after coupling to
the radiation field then it is unstable, provided the coupling constant is
sufficiently small (depending on the temperature).
The result is proven by analyzing the spectrum of the thermal Hamiltonian
(Liouvillian) of the system within the framework of -dynamical systems. A
key element of our spectral analysis is the positive commutator method
On propagation of information in quantum many-body systems
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 based on a maximal velocity bound,
which states that the many-body evolution stays, up to small leaking
probability tails, within a light cone of the support of the initial
conditions. This estimate is used to prove the light-cone approximation of
dynamics and Lieb-Robinson-type bound, which in turn yield the results above.
Our conditions cover long-range interactions. The main results of this paper as
well as some key steps of the proofs were first presented in [36].Comment: updated reference [36] M. Lemm, C. Rubiliani, I. M. Sigal, and J.
Zhang, Information propagation in long-range quantum many-body systems, Phys.
Rev. A, To appear (2023
Instability of electroweak homogeneous vacua in strong magnetic fields
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. We study the WS vacuum solutions exhibiting a
non-vanishing average magnetic field, , and prove that (i) there is a
magnetic field threshold such that for , the vacua are
translationally invariant (and the magnetic field is constant), while, for
, they are not, (ii) for , there are
non-translationally invariant solutions with lower energy per unit volume and
with the discrete translational symmetry of a 2D lattice in the plane
transversal to , and (iii) the lattice minimizing the energy per unit
volume approaches the hexagonal one as the magnetic field strength approaches
the threshold .
In the absence of particles, the Weinberg-Salam model reduces to the
Yang-Mills-Higgs (YMH) equations for the gauge group . Thus our results
can be rephrased as the corresponding statements about the -YMH equation
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