615 research outputs found
On Some Open Problems in Many-Electron Theory
Mel Levy and Elliott Lieb are two of the most prominent researchers who have
dedicated their efforts to the investigation of fundamental questions in
many-electron theory. Their results have not only revolutionized the
theoretical approach of the field, but, directly or indirectly, allowed for a
quantum jump in the computational treatment of realistic systems as well. For
this reason, at the conclusion of our book where the subject is treated across
different disciplines, we have asked Mel Levy and Elliott Lieb to provide us
with some open problems, which they believe will be a worth challenge for the
future also in the perspective of a synergy among the various disciplines.Comment: "Epilogue" chapter in "Many-Electron Approaches in Physics, Chemistry
and Mathematics: A Multidisciplinary View", Volker Bach and Luigi Delle Site
Eds. pages 411-416; Book Series: Mathematical Physics Studies, Springer
International Publishing Switzerland, 2014. The original title has been
modified in order to clarify the subject of the chapter out of the context of
the boo
Domain structure of ultrathin ferromagnetic elements in the presence of Dzyaloshinskii–Moriya interaction
Including a phase in the Bethe equations of the Hubbard model
We compute the Bethe equations of generalized Hubbard models, and study their
thermodynamical limit. We argue how they can be connected to the ones found in
the context of AdS/CFT correspondence, in particular with the so-called
dressing phase problem. We also show how the models can be interpreted, in
condensed matter physics, as integrable multi-leg Hubbard models.Comment: 30 page
Mean-field evolution of fermions with singular interaction
We consider a system of N fermions in the mean-field regime interacting
though an inverse power law potential , for
. We prove the convergence of a solution of the many-body
Schr\"{o}dinger equation to a solution of the time-dependent Hartree-Fock
equation in the sense of reduced density matrices. We stress the dependence on
the singularity of the potential in the regularity of the initial data. The
proof is an adaptation of [22], where the case is treated.Comment: 16 page
Field evolution of the magnetic structures in ErTiO through the critical point
We have measured neutron diffraction patterns in a single crystal sample of
the pyrochlore compound ErTiO in the antiferromagnetic phase
(T=0.3\,K), as a function of the magnetic field, up to 6\,T, applied along the
[110] direction. We determine all the characteristics of the magnetic structure
throughout the quantum critical point at =2\,T. As a main result, all Er
moments align along the field at and their values reach a minimum. Using
a four-sublattice self-consistent calculation, we show that the evolution of
the magnetic structure and the value of the critical field are rather well
reproduced using the same anisotropic exchange tensor as that accounting for
the local paramagnetic susceptibility. In contrast, an isotropic exchange
tensor does not match the moment variations through the critical point. The
model also accounts semi-quantitatively for other experimental data previously
measured, such as the field dependence of the heat capacity, energy of the
dispersionless inelastic modes and transition temperature.Comment: 7 pages; 8 figure
Pauli's Principle in Probe Microscopy
Exceptionally clear images of intramolecular structure can be attained in
dynamic force microscopy through the combination of a passivated tip apex and
operation in what has become known as the "Pauli exclusion regime" of the
tip-sample interaction. We discuss, from an experimentalist's perspective, a
number of aspects of the exclusion principle which underpin this ability to
achieve submolecular resolution. Our particular focus is on the origins,
history, and interpretation of Pauli's principle in the context of interatomic
and intermolecular interactions.Comment: This is a chapter from "Imaging and Manipulation of Adsorbates using
Dynamic Force Microscopy", a book which is part of the "Advances in Atom and
Single Molecule Machines" series published by Springer
[http://www.springer.com/series/10425]. To be published late 201
Smooth Entropy in Axiomatic Thermodynamics
Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic constituents. We establish a connection between these two approaches by means of a new axiomatic framework that can take errors and imprecisions into account. This link extends to systems of arbitrary sizes including very small systems, for which the treatment of imprecisions is pertinent to any realistic situation. Based on this, we identify the quantities that characterise whether certain thermodynamic processes are possible with entropy measures from information theory. In the error-tolerant case, these entropies are so-called smooth min and max entropies. Our considerations further show that in an appropriate macroscopic limit there is a single entropy measure that characterises which state transformations are possible. In the case of many independent copies of a system (the so-called i.i.d. regime), the relevant quantity is the von Neumann entropy. Transformations among microcanonical states are characterised by the Boltzmann entropy
Blow-up profile of rotating 2D focusing Bose gases
We consider the Gross-Pitaevskii equation describing an attractive Bose gas
trapped to a quasi 2D layer by means of a purely harmonic potential, and which
rotates at a fixed speed of rotation . First we study the behavior of
the ground state when the coupling constant approaches , the critical
strength of the cubic nonlinearity for the focusing nonlinear Schr{\"o}dinger
equation. We prove that blow-up always happens at the center of the trap, with
the blow-up profile given by the Gagliardo-Nirenberg solution. In particular,
the blow-up scenario is independent of , to leading order. This
generalizes results obtained by Guo and Seiringer (Lett. Math. Phys., 2014,
vol. 104, p. 141--156) in the non-rotating case. In a second part we consider
the many-particle Hamiltonian for bosons, interacting with a potential
rescaled in the mean-field manner w\int\_{\mathbb{R}^2} w(x) dx = 1\beta < 1/2a\_N \to a\_*N \to \infty$
Degenerate Stars and Gravitational Collapse in AdS/CFT
We construct composite CFT operators from a large number of fermionic primary
fields corresponding to states that are holographically dual to a zero
temperature Fermi gas in AdS space. We identify a large N regime in which the
fermions behave as free particles. In the hydrodynamic limit the Fermi gas
forms a degenerate star with a radius determined by the Fermi level, and a mass
and angular momentum that exactly matches the boundary calculations. Next we
consider an interacting regime, and calculate the effect of the gravitational
back-reaction on the radius and the mass of the star using the
Tolman-Oppenheimer-Volkoff equations. Ignoring other interactions, we determine
the "Chandrasekhar limit" beyond which the degenerate star (presumably)
undergoes gravitational collapse towards a black hole. This is interpreted on
the boundary as a high density phase transition from a cold baryonic phase to a
hot deconfined phase.Comment: 75 page
Two remarks on generalized entropy power inequalities
This note contributes to the understanding of generalized entropy power
inequalities. Our main goal is to construct a counter-example regarding
monotonicity and entropy comparison of weighted sums of independent identically
distributed log-concave random variables. We also present a complex analogue of
a recent dependent entropy power inequality of Hao and Jog, and give a very
simple proof.Comment: arXiv:1811.00345 is split into 2 papers, with this being on
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