27,059 research outputs found
Renormalization group study of the four-body problem
We perform a renormalization group analysis of the non-relativistic
four-boson problem by means of a simple model with pointlike three- and
four-body interactions. We investigate in particular the unitarity point where
the scattering length is infinite and all energies are at the atom threshold.
We find that the four-body problem behaves truly universally, independent of
any four-body parameter. Our findings confirm the recent conjectures of Platter
et al. and von Stecher et al. that the four-body problem is universal, now also
from a renormalization group perspective. We calculate the corresponding
relations between the four- and three-body bound states, as well as the full
bound state spectrum and comment on the influence of effective range
corrections.Comment: 11 pages, 6 figures; v2: revised and published versio
Efimov physics from the functional renormalization group
Few-body physics related to the Efimov effect is discussed using the
functional renormalization group method. After a short review of
renormalization in its modern formulation we apply this formalism to the
description of scattering and bound states in few-body systems of identical
bosons and distinguishable fermions with two and three components. The Efimov
effect leads to a limit cycle in the renormalization group flow. Recently
measured three-body loss rates in an ultracold Fermi gas Li atoms are
explained within this framework. We also discuss briefly the relation to the
many-body physics of the BCS-BEC crossover for two-component fermions and the
formation of a trion phase for the case of three species.Comment: 28 pages, 13 figures, invited contribution to a special issue of
"Few-Body Systems" devoted to Efimov physics, published versio
Efimov effect from functional renormalization
We apply a field-theoretic functional renormalization group technique to the
few-body (vacuum) physics of non-relativistic atoms near a Feshbach resonance.
Three systems are considered: one-component bosons with U(1) symmetry,
two-component fermions with U(1)\times SU(2) symmetry and three-component
fermions with U(1) \times SU(3) symmetry. We focus on the scale invariant
unitarity limit for infinite scattering length. The exact solution for the
two-body sector is consistent with the unitary fixed point behavior for all
considered systems. Nevertheless, the numerical three-body solution in the
s-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3)
fermions. The Efimov parameter for the one-component bosons and the
three-component fermions is found to be approximately s=1.006, consistent with
the result of Efimov.Comment: 21 pages, 6 figures, minor changes, published versio
Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects
We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation
in phase space. We demonstrate that it accommodates the phase space
dynamics of low dimensional dissipative systems such as the much studied Lorenz
and R\"{o}ssler Strange attractors, as well as the more recent constructions of
Chen and Leipnik-Newton. The rotational, volume preserving part of the flow
preserves in time a family of two intersecting surfaces, the so called {\em
Nambu Hamiltonians}. They foliate the entire phase space and are, in turn,
deformed in time by Dissipation which represents their irrotational part of the
flow. It is given by the gradient of a scalar function and is responsible for
the emergence of the Strange Attractors.
Based on our recent work on Quantum Nambu Mechanics, we provide an explicit
quantization of the Lorenz attractor through the introduction of
Non-commutative phase space coordinates as Hermitian matrices in
. They satisfy the commutation relations induced by one of the two
Nambu Hamiltonians, the second one generating a unique time evolution.
Dissipation is incorporated quantum mechanically in a self-consistent way
having the correct classical limit without the introduction of external degrees
of freedom. Due to its volume phase space contraction it violates the quantum
commutation relations. We demonstrate that the Heisenberg-Nambu evolution
equations for the Quantum Lorenz system give rise to an attracting ellipsoid in
the dimensional phase space.Comment: 35 pages, 4 figures, LaTe
Pascual Jordan's resolution of the conundrum of the wave-particle duality of light
In 1909, Einstein derived a formula for the mean square energy fluctuation in
black-body radiation. This formula is the sum of a wave term and a particle
term. In a key contribution to the 1925 Dreimaennerarbeit with Born and
Heisenberg, Jordan showed that one recovers both terms in a simple model of
quantized waves. So the two terms do not require separate mechanisms but arise
from a single consistent dynamical framework. Several authors have argued that
various infinities invalidate Jordan's conclusions. In this paper, we defend
Jordan's argument against such criticism. In particular, we note that the
fluctuation in a narrow frequency range, which is what Jordan calculated, is
perfectly finite. We also note, however, that Jordan's argument is incomplete.
In modern terms, Jordan calculated the quantum uncertainty in the energy of a
subsystem in an energy eigenstate of the whole system, whereas the thermal
fluctuation is the average of this quantity over an ensemble of such states.
Still, our overall conclusion is that Jordan's argument is basically sound and
that he deserves credit for resolving a major conundrum in the development of
quantum physics.Comment: This paper was written as part of a joint project in the history of
quantum physics of the Max Planck Institut fuer Wissenschaftsgeschichte and
the Fritz Haber Institut in Berli
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