119 research outputs found
Entanglement and localization of wavefunctions
We review recent works that relate entanglement of random vectors to their
localization properties. In particular, the linear entropy is related by a
simple expression to the inverse participation ratio, while next orders of the
entropy of entanglement contain information about e.g. the multifractal
exponents. Numerical simulations show that these results can account for the
entanglement present in wavefunctions of physical systems.Comment: 6 pages, 4 figures, to appear in the proceedings of the NATO Advanced
Research Workshop 'Recent Advances in Nonlinear Dynamics and Complex System
Physics', Tashkent, Uzbekistan, 200
Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
The fluctuations in nonequilibrium systems are under intense theoretical and
experimental investigation. Topical ``fluctuation relations'' describe
symmetries of the statistical properties of certain observables, in a variety
of models and phenomena. They have been derived in deterministic and, later, in
stochastic frameworks. Other results first obtained for stochastic processes,
and later considered in deterministic dynamics, describe the temporal evolution
of fluctuations. The field has grown beyond expectation: research works and
different perspectives are proposed at an ever faster pace. Indeed,
understanding fluctuations is important for the emerging theory of
nonequilibrium phenomena, as well as for applications, such as those of
nanotechnological and biophysical interest. However, the links among the
different approaches and the limitations of these approaches are not fully
understood. We focus on these issues, providing: a) analysis of the theoretical
models; b) discussion of the rigorous mathematical results; c) identification
of the physical mechanisms underlying the validity of the theoretical
predictions, for a wide range of phenomena.Comment: 44 pages, 2 figures. To appear in Nonlinearity (2007
Chaos and Complexity of quantum motion
The problem of characterizing complexity of quantum dynamics - in particular
of locally interacting chains of quantum particles - will be reviewed and
discussed from several different perspectives: (i) stability of motion against
external perturbations and decoherence, (ii) efficiency of quantum simulation
in terms of classical computation and entanglement production in operator
spaces, (iii) quantum transport, relaxation to equilibrium and quantum mixing,
and (iv) computation of quantum dynamical entropies. Discussions of all these
criteria will be confronted with the established criteria of integrability or
quantum chaos, and sometimes quite surprising conclusions are found. Some
conjectures and interesting open problems in ergodic theory of the quantum many
problem are suggested.Comment: 45 pages, 22 figures, final version, at press in J. Phys. A, special
issue on Quantum Informatio
From thermal rectifiers to thermoelectric devices
We discuss thermal rectification and thermoelectric energy conversion from
the perspective of nonequilibrium statistical mechanics and dynamical systems
theory. After preliminary considerations on the dynamical foundations of the
phenomenological Fourier law in classical and quantum mechanics, we illustrate
ways to control the phononic heat flow and design thermal diodes. Finally, we
consider the coupled transport of heat and charge and discuss several general
mechanisms for optimizing the figure of merit of thermoelectric efficiency.Comment: 42 pages, 22 figures, review paper, to appear in the Springer Lecture
Notes in Physics volume "Thermal transport in low dimensions: from
statistical physics to nanoscale heat transfer" (S. Lepri ed.
Entropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems
Highly excited many-particle states in quantum systems such as nuclei, atoms,
quantum dots, spin systems, quantum computers etc., can be considered as
``chaotic'' superpositions of mean-field basis states (Slater determinants,
products of spin or qubit states). This is due to a very high level density of
many-body states that are easily mixed by a residual interaction between
particles (quasi-particles). For such systems, we have derived simple
analytical expressions for the time dependence of energy width of wave packets,
as well as for the entropy, number of principal basis components and inverse
participation ratio, and tested them in numerical experiments. It is shown that
the energy width increases linearly and very quickly saturates.
The entropy of a system increases quadratically, at small
times, and after, can grow linearly, , before the saturation.
Correspondingly, the number of principal components determined by the entropy,
, or by the inverse participation ratio, increases
exponentially fast before the saturation. These results are explained in terms
of a cascade model which describes the flow of excitation in the Fock space of
basis components. Finally, a striking phenomenon of damped oscillations in the
Fock space at the transition to an equilibrium is discussed.Comment: RevTex, 14 pages including 12 eps-figure
Finite thermal conductivity in 1D models having zero Lyapunov exponents
Heat conduction in three types of 1D channels are studied. The channels
consist of two parallel walls, right triangles as scattering obstacles, and
noninteracting particles. The triangles are placed along the walls in three
different ways: (a) periodic, (b) disordered in height, and (c) disordered in
position. The Lyapunov exponents in all three models are zero because of the
flatness of triangle sides. It is found numerically that the temperature
gradient can be formed in all three channels, but the Fourier heat law is
observed only in two disordered ones. The results show that there might be no
direct connection between chaos (in the sense of positive Lyapunov exponent)
and the normal thermal conduction.Comment: 4 PRL page
Ground-State Magnetization for Interacting Fermions in a Disordered Potential : Kinetic Energy, Exchange Interaction and Off-Diagonal Fluctuations
We study a model of interacting fermions in a disordered potential, which is
assumed to generate uniformly fluctuating interaction matrix elements. We show
that the ground state magnetization is systematically decreased by off-diagonal
fluctuations of the interaction matrix elements. This effect is neglected in
the Stoner picture of itinerant ferromagnetism in which the ground-state
magnetization is simply determined by the balance between ferromagnetic
exchange and kinetic energy, and increasing the interaction strength always
favors ferromagnetism. The physical origin of the demagnetizing effect of
interaction fluctuations is the larger number of final states available for
interaction-induced scattering in the lower spin sectors of the Hilbert space.
We analyze the energetic role played by these fluctuations in the limits of
small and large interaction . In the small limit we do second-order
perturbation theory and identify explicitly transitions which are allowed for
minimal spin and forbidden for higher spin. These transitions then on average
lower the energy of the minimal spin ground state with respect to higher spin.
For large interactions we amplify on our earlier work [Ph. Jacquod and A.D.
Stone, Phys. Rev. Lett. 84, 3938 (2000)] which showed that minimal spin is
favored due to a larger broadening of the many-body density of states in the
low-spin sectors. Numerical results are presented in both limits.Comment: 35 pages, 24 figures - final, shortened version, to appear in
Physical Review
A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade
We provide a framework for analyzing the problem of interacting electrons in
a ballistic quantum dot with chaotic boundary conditions within an energy
(the Thouless energy) of the Fermi energy. Within this window we show that the
interactions can be characterized by Landau Fermi liquid parameters. When ,
the dimensionless conductance of the dot, is large, we find that the disordered
interacting problem can be solved in a saddle-point approximation which becomes
exact as (as in a large-N theory). The infinite theory shows a
transition to a strong-coupling phase characterized by the same order parameter
as in the Pomeranchuk transition in clean systems (a spontaneous
interaction-induced Fermi surface distortion), but smeared and pinned by
disorder. At finite , the two phases and critical point evolve into three
regimes in the plane -- weak- and strong-coupling regimes separated
by crossover lines from a quantum-critical regime controlled by the quantum
critical point. In the strong-coupling and quantum-critical regions, the
quasiparticle acquires a width of the same order as the level spacing
within a few 's of the Fermi energy due to coupling to collective
excitations. In the strong coupling regime if is odd, the dot will (if
isolated) cross over from the orthogonal to unitary ensemble for an
exponentially small external flux, or will (if strongly coupled to leads) break
time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we
are treating charge-channel instabilities in spinful systems, leaving
spin-channel instabilities for future work. No substantive results are
change
Adaptation and Convergent Evolution within the Jamesonia-Eriosorus Complex in High-Elevation Biodiverse Andean Hotspots
The recent uplift of the tropical Andes (since the late Pliocene or early Pleistocene) provided extensive ecological opportunity for evolutionary radiations. We test for phylogenetic and morphological evidence of adaptive radiation and convergent evolution to novel habitats (exposed, high-altitude páramo habitats) in the Andean fern genera Jamesonia and Eriosorus. We construct time-calibrated phylogenies for the Jamesonia-Eriosorus clade. We then use recent phylogenetic comparative methods to test for evolutionary transitions among habitats, associations between habitat and leaf morphology, and ecologically driven variation in the rate of morphological evolution. Páramo species (Jamesonia) display morphological adaptations consistent with convergent evolution in response to the demands of a highly exposed environment but these adaptations are associated with microhabitat use rather than the páramo per se. Species that are associated with exposed microhabitats (including Jamesonia and Eriorsorus) are characterized by many but short pinnae per frond whereas species occupying sheltered microhabitats (primarily Eriosorus) have few but long pinnae per frond. Pinnae length declines more rapidly with altitude in sheltered species. Rates of speciation are significantly higher among páramo than non-páramo lineages supporting the hypothesis of adaptation and divergence in the unique Páramo biodiversity hotspot
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