1,063 research outputs found
Fermi Edge Resonances in Non-equilibrium States of Fermi Gases
We formulate the problem of the Fermi Edge Singularity in non-equilibrium
states of a Fermi gas as a matrix Riemann-Hilbert problem with an integrable
kernel. This formulation is the most suitable for studying the singular
behavior at each edge of non-equilibrium Fermi states by means of the method of
steepest descent, and also reveals the integrable structure of the problem. We
supplement this result by extending the familiar approach to the problem of the
Fermi Edge Singularity via the bosonic representation of the electronic
operators to non-equilibrium settings. It provides a compact way to extract the
leading asymptotes.Comment: Accepted for publication, J. Phys.
Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas
A semiclassical wave-packet propagating in a dissipationless Fermi gas
inevitably enters a "gradient catastrophe" regime, where an initially smooth
front develops large gradients and undergoes a dramatic shock wave phenomenon.
The non-linear effects in electronic transport are due to the curvature of the
electronic spectrum at the Fermi surface. They can be probed by a sudden
switching of a local potential. In equilibrium, this process produces a large
number of particle-hole pairs, a phenomenon closely related to the
Orthogonality Catastrophe. We study a generalization of this phenomenon to the
non-equilibrium regime and show how the Orthogonality Catastrophe cures the
Gradient Catastrophe, providing a dispersive regularization mechanism. We show
that a wave packet overturns and collapses into modulated oscillations with the
wave vector determined by the height of the initial wave. The oscillations
occupy a growing region extending forward with velocity proportional to the
initial height of the packet. We derive a fundamental equation for the
transition rates (MKP-equation) and solve it by means of the Whitham modulation
theory.Comment: 5 pages, 1 figure, revtex4, pr
Fermi distribution of semicalssical non-eqilibrium Fermi states
When a classical device suddenly perturbs a degenerate Fermi gas a
semiclassical non-equilibrium Fermi state arises. Semiclassical Fermi states
are characterized by a Fermi energy or Fermi momentum that slowly depends on
space or/and time. We show that the Fermi distribution of a semiclassical Fermi
state has a universal nature. It is described by Airy functions regardless of
the details of the perturbation. In this letter we also give a general
discussion of coherent Fermi states
Gradient Catastrophe and Fermi Edge Resonances in Fermi Gas
A smooth spatial disturbance of the Fermi surface in a Fermi gas inevitably
becomes sharp. This phenomenon, called {\it the gradient catastrophe}, causes
the breakdown of a Fermi sea to disconnected parts with multiple Fermi points.
We study how the gradient catastrophe effects probing the Fermi system via a
Fermi edge singularity measurement. We show that the gradient catastrophe
transforms the single-peaked Fermi-edge singularity of the tunneling (or
absorption) spectrum to a set of multiple asymmetric singular resonances. Also
we gave a mathematical formulation of FES as a matrix Riemann-Hilbert problem
Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
Using the Calogero model as an example, we show that the transport in
interacting non-dissipative electronic systems is essentially non-linear.
Non-linear effects are due to the curvature of the electronic spectrum near the
Fermi energy. As is typical for non-linear systems, propagating wave packets
are unstable. At finite time shock wave singularities develop, the wave packet
collapses, and oscillatory features arise. They evolve into regularly
structured localized pulses carrying a fractionally quantized charge - {\it
soliton trains}. We briefly discuss perspectives of observation of Quantum
Shock Waves in edge states of Fractional Quantum Hall Effect and a direct
measurement of the fractional charge
The experience of enchantment in human-computer interaction
Improving user experience is becoming something of a rallying call in human–computer interaction but experience is not a unitary thing. There are varieties of experiences, good and bad, and we need to characterise these varieties if we are to improve user experience. In this paper we argue that enchantment is a useful concept to facilitate closer relationships between people and technology. But enchantment is a complex concept in need of some clarification. So we explore how enchantment has been used in the discussions of technology and examine experiences of film and cell phones to see how enchantment with technology is possible. Based on these cases, we identify the sensibilities that help designers design for enchantment, including the specific sensuousness of a thing, senses of play, paradox and openness, and the potential for transformation. We use these to analyse digital jewellery in order to suggest how it can be made more enchanting. We conclude by relating enchantment to varieties of experience.</p
Quantum Hall transitions: An exact theory based on conformal restriction
We revisit the problem of the plateau transition in the integer quantum Hall
effect. Here we develop an analytical approach for this transition, based on
the theory of conformal restriction. This is a mathematical theory that was
recently developed within the context of the Schramm-Loewner evolution which
describes the stochastic geometry of fractal curves and other stochastic
geometrical fractal objects in 2D space. Observables elucidating the connection
with the plateau transition include the so-called point-contact conductances
(PCCs) between points on the boundary of the sample, described within the
language of the Chalker-Coddington network model. We show that the
disorder-averaged PCCs are characterized by classical probabilities for certain
geometric objects in the plane (pictures), occurring with positive statistical
weights, that satisfy the crucial restriction property with respect to changes
in the shape of the sample with absorbing boundaries. Upon combining this
restriction property with the expected conformal invariance at the transition
point, we employ the mathematical theory of conformal restriction measures to
relate the disorder-averaged PCCs to correlation functions of primary operators
in a conformal field theory (of central charge ). We show how this can be
used to calculate these functions in a number of geometries with various
boundary conditions. Since our results employ only the conformal restriction
property, they are equally applicable to a number of other critical disordered
electronic systems in 2D. For most of these systems, we also predict exact
values of critical exponents related to the spatial behavior of various
disorder-averaged PCCs.Comment: Published versio
Viscous fingering and a shape of an electronic droplet in the Quantum Hall regime
We show that the semiclassical dynamics of an electronic droplet confined in
the plane in a quantizing inhomogeneous magnetic field in the regime when the
electrostatic interaction is negligible is similar to viscous (Saffman-Taylor)
fingering on the interface between two fluids with different viscosities
confined in a Hele-Shaw cell. Both phenomena are described by the same
equations with scales differing by a factor of up to . We also report
the quasiclassical wave function of the droplet in an inhomogeneous magnetic
field.Comment: 4 pages, 1 eps figure include
On harmonic measure of critical curves
Fractal geometry of critical curves appearing in 2D critical systems is
characterized by their harmonic measure. For systems described by conformal
field theories with central charge , scaling exponents of
harmonic measure have been computed by B. Duplantier [Phys. Rev. Lett. {\bf
84}, 1363 (2000)] by relating the problem to boundary two-dimensional gravity.
We present a simple argument that allows us to connect harmonic measure of
critical curves to operators obtained by fusion of primary fields, and compute
characteristics of fractal geometry by means of regular methods of conformal
field theory. The method is not limited to theories with .Comment: Some more correction
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