3,841 research outputs found
Universal quench dynamics of interacting quantum impurity systems
The equilibrium physics of quantum impurities frequently involves a universal
crossover from weak to strong reservoir-impurity coupling, characterized by
single-parameter scaling and an energy scale (Kondo temperature) that
breaks scale invariance. For the non-interacting resonant level model, the
non-equilibrium time evolution of the Loschmidt echo after a local quantum
quench was recently computed explicitely [R. Vasseur, K. Trinh, S. Haas, and H.
Saleur, Phys. Rev. Lett. 110, 240601 (2013)]. It shows single-parameter scaling
with variable . Here, we scrutinize whether similar universal dynamics
can be observed in various interacting quantum impurity systems. Using density
matrix and functional renormalization group approaches, we analyze the time
evolution resulting from abruptly coupling two non-interacting Fermi or
interacting Luttinger liquid leads via a quantum dot or a direct link. We also
consider the case of a single Luttinger liquid lead suddenly coupled to a
quantum dot. We investigate whether the field theory predictions for the
universal scaling as well as for the large time behavior successfully describe
the time evolution of the Loschmidt echo and the entanglement entropy of
microscopic models.Comment: 14 pages, 10 figure
Universal nonequilibrium signatures of Majorana zero modes in quench dynamics
The quantum evolution after a metallic lead is suddenly connected to an
electron system contains information about the excitation spectrum of the
combined system. We exploit this type of "quantum quench" to probe the presence
of Majorana fermions at the ends of a topological superconducting wire. We
obtain an algebraically decaying overlap (Loschmidt echo) for large times after the quench, with
a universal critical exponent =1/4 that is found to be remarkably
robust against details of the setup, such as interactions in the normal lead,
the existence of additional lead channels or the presence of bound levels
between the lead and the superconductor. As in recent quantum dot experiments,
this exponent could be measured by optical absorption, offering a new signature
of Majorana zero modes that is distinct from interferometry and tunneling
spectroscopy.Comment: 9 pages + appendices, 4 figures. v3: published versio
The periodic sl(2|1) alternating spin chain and its continuum limit as a bulk Logarithmic Conformal Field Theory at c=0
The periodic sl(2|1) alternating spin chain encodes (some of) the properties
of hulls of percolation clusters, and is described in the continuum limit by a
logarithmic conformal field theory (LCFT) at central charge c=0. This theory
corresponds to the strong coupling regime of a sigma model on the complex
projective superspace , and the spectrum of critical exponents can be
obtained exactly. In this paper we push the analysis further, and determine the
main representation theoretic (logarithmic) features of this continuum limit by
extending to the periodic case the approach of [N. Read and H. Saleur, Nucl.
Phys. B 777 316 (2007)]. We first focus on determining the representation
theory of the finite size spin chain with respect to the algebra of local
energy densities provided by a representation of the affine Temperley-Lieb
algebra at fugacity one. We then analyze how these algebraic properties carry
over to the continuum limit to deduce the structure of the space of states as a
representation over the product of left and right Virasoro algebras. Our main
result is the full structure of the vacuum module of the theory, which exhibits
Jordan cells of arbitrary rank for the Hamiltonian.Comment: 69pp, 8 fig
Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model
The two-dimensional Potts model can be studied either in terms of the
original Q-component spins, or in the geometrical reformulation via
Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for
arbitrary real values of Q by construction, it was only shown very recently
that the spin representation can be promoted to the same level of generality.
In this paper we show how to define the Potts model in terms of observables
that simultaneously keep track of the spin and FK degrees of freedom. This is
first done algebraically in terms of a transfer matrix that couples three
different representations of a partition algebra. Using this, one can study
correlation functions involving any given number of propagating spin clusters
with prescribed colours, each of which contains any given number of distinct FK
clusters. For 0 <= Q <= 4 the corresponding critical exponents are all of the
Kac form h_{r,s}, with integer indices r,s that we determine exactly both in
the bulk and in the boundary versions of the problem. In particular, we find
that the set of points where an FK cluster touches the hull of its surrounding
spin cluster has fractal dimension d_{2,1} = 2 - 2 h_{2,1}. If one constrains
this set to points where the neighbouring spin cluster extends to infinity, we
show that the dimension becomes d_{1,3} = 2 - 2 h_{1,3}. Our results are
supported by extensive transfer matrix and Monte Carlo computations.Comment: 15 pages, 3 figures, 2 table
Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: a local mean-field analysis
We show how microstructure can arise in first-order ferroelastic structural
transitions, in two and three spatial dimensions, through a local meanfield
approximation of their pseudospin hamiltonians, that include anisotropic
elastic interactions. Such transitions have symmetry-selected physical strains
as their -component order parameters, with Landau free energies that
have a single zero-strain 'austenite' minimum at high temperatures, and
spontaneous-strain 'martensite' minima of structural variants at low
temperatures. In a reduced description, the strains at Landau minima induce
temperature-dependent, clock-like hamiltonians, with
-component strain-pseudospin vectors pointing to
discrete values (including zero). We study elastic texturing in five such
first-order structural transitions through a local meanfield approximation of
their pseudospin hamiltonians, that include the powerlaw interactions. As a
prototype, we consider the two-variant square/rectangle transition, with a
one-component, pseudospin taking values of , as in a
generalized Blume-Capel model. We then consider transitions with two-component
() pseudospins: the equilateral to centred-rectangle ();
the square to oblique polygon (); the triangle to oblique ()
transitions; and finally the 3D cubic to tetragonal transition (). The
local meanfield solutions in 2D and 3D yield oriented domain-walls patterns as
from continuous-variable strain dynamics, showing the discrete-variable models
capture the essential ferroelastic texturings. Other related hamiltonians
illustrate that structural-transitions in materials science can be the source
of interesting spin models in statistical mechanics.Comment: 15 pages, 9 figure
Logarithmic observables in critical percolation
Although it has long been known that the proper quantum field theory
description of critical percolation involves a logarithmic conformal field
theory (LCFT), no direct consequence of this has been observed so far.
Representing critical bond percolation as the Q = 1 limit of the Q-state Potts
model, and analyzing the underlying S_Q symmetry of the Potts spins, we
identify a class of simple observables whose two-point functions scale
logarithmically for Q = 1. The logarithm originates from the mixing of the
energy operator with a logarithmic partner that we identify as the field that
creates two propagating clusters. In d=2 dimensions this agrees with general
LCFT results, and in particular the universal prefactor of the logarithm can be
computed exactly. We confirm its numerical value by extensive Monte-Carlo
simulations.Comment: 11 pages, 2 figures. V2: as publishe
Synchronous dynamics of zooplankton competitors prevail in temperate lake ecosystems
Although competing species are expected to exhibit compensatory dynamics (negative temporal covariation), empirical work has demonstrated that competitive communities often exhibit synchronous dynamics (positive temporal covariation). This has led to the suggestion that environmental forcing dominates species dynamics; however, synchronous and compensatory dynamics may appear at different length scales and/or at different times, making it challenging to identify their relative importance. We compiled 58 long-term datasets of zooplankton abundance in north-temperate and sub-tropical lakes and used wavelet analysis to quantify general patterns in the times and scales at which synchronous/compensatory dynamics dominated zooplankton communities in different regions and across the entire dataset. Synchronous dynamics were far more prevalent at all scales and times and were ubiquitous at the annual scale. Although we found compensatory dynamics in approximately 14% of all combinations of time period/scale/lake, there were no consistent scales or time periods during which compensatory dynamics were apparent across different regions. Our results suggest that the processes driving compensatory dynamics may be local in their extent, while those generating synchronous dynamics operate at much larger scales. This highlights an important gap in our understanding of the interaction between environmental and biotic forces that structure communities
Incompressible flow in porous media with fractional diffusion
In this paper we study the heat transfer with a general fractional diffusion
term of an incompressible fluid in a porous medium governed by Darcy's law. We
show formation of singularities with infinite energy and for finite energy we
obtain existence and uniqueness results of strong solutions for the
sub-critical and critical cases. We prove global existence of weak solutions
for different cases. Moreover, we obtain the decay of the solution in ,
for any , and the asymptotic behavior is shown. Finally, we prove the
existence of an attractor in a weak sense and, for the sub-critical dissipative
case with , we obtain the existence of the global attractor
for the solutions in the space for any
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