256 research outputs found
Quantum phase transitions from topology in momentum space
Many quantum condensed matter systems are strongly correlated and strongly
interacting fermionic systems, which cannot be treated perturbatively. However,
physics which emerges in the low-energy corner does not depend on the
complicated details of the system and is relatively simple. It is determined by
the nodes in the fermionic spectrum, which are protected by topology in
momentum space (in some cases, in combination with the vacuum symmetry). Close
to the nodes the behavior of the system becomes universal; and the universality
classes are determined by the toplogical invariants in momentum space. When one
changes the parameters of the system, the transitions are expected to occur
between the vacua with the same symmetry but which belong to different
universality classes. Different types of quantum phase transitions governed by
topology in momentum space are discussed in this Chapter. They involve Fermi
surfaces, Fermi points, Fermi lines, and also the topological transitions
between the fully gapped states. The consideration based on the momentum space
topology of the Green's function is general and is applicable to the vacua of
relativistic quantum fields. This is illustrated by the possible quantum phase
transition governed by topology of nodes in the spectrum of elementary
particles of Standard Model.Comment: 45 pages, 17 figures, 83 references, Chapter for the book "Quantum
Simulations via Analogues: From Phase Transitions to Black Holes", to appear
in Springer lecture notes in physics (LNP
Wavefunction topology of two-dimensional time-reversal symmetric superconductors
We discuss the topology of the wavefunctions of two-dimensional time-reversal
symmetric superconductors. We consider (a) the planar state, (b) a system with
broken up-down reflection symmetry, and (c) a system with general spin-orbit
interaction. We show explicitly how the relative sign of the order parameter on
the two Fermi surfaces affects this topology, and clarify the meaning of the
classification for these topological states.Comment: only the Introduction has been modified from v
Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition
Cylindrical algebraic decomposition(CAD) is a key tool in computational
algebraic geometry, particularly for quantifier elimination over real-closed
fields. When using CAD, there is often a choice for the ordering placed on the
variables. This can be important, with some problems infeasible with one
variable ordering but easy with another. Machine learning is the process of
fitting a computer model to a complex function based on properties learned from
measured data. In this paper we use machine learning (specifically a support
vector machine) to select between heuristics for choosing a variable ordering,
outperforming each of the separate heuristics.Comment: 16 page
Iordanskii Force and the Gravitational Aharonov-Bohm effect for a Moving Vortex
I discuss the scattering of phonons by a vortex moving with respect to a
superfluid condensate. This allows us to test the compatibility of the
scattering-theory derivation of the Iordanskii force with the galilean
invariance of the underlying fluid dynamics. In order to obtain the correct
result we must retain terms in the sound-wave equation, and this
reinforces the interpretation, due to Volovik, of the Iordanskii force as an
analogue of the gravitational Bohm-Aharonov effect.Comment: 20 pages, LaTe
Spectrum of the Vortex Bound States of the Dirac and Schrodinger Hamiltonian in the presence of Superconducting Gaps
We investigate the vortex bound states both Schrodinger and Dirac Hamiltonian
with the s-wave superconducting pairing gap by solving the mean-field
Bogoliubov-de-Gennes equations. The exact vortex bound states spectrum is
numerically determined by the integration method, and also accompanied by the
quasi-classical analysis. It is found that the bound state energies is
proportional to the vortex angular momentum when the chemical potential is
large enough. By applying the external magnetic field, the vortex bound state
energies of the Dirac Hamiltonian are almost unchanged; whereas the energy
shift of the Schrodinger Hamiltonian is proportional to the magnetic field.
These qualitative differences may serve as an indirect evidence of the
existence of Majorana fermions in which the zero mode exists in the case of the
Dirac Hamiltonian only.Comment: 8 pages, 9 figure
On Slow Light as a Black Hole Analogue
Although slow light (electromagnetically induced transparency) would seem an
ideal medium in which to institute a ``dumb hole'' (black hole analog), it
suffers from a number of problems. We show that the high phase velocity in the
slow light regime ensures that the system cannot be used as an analog
displaying Hawking radiation. Even though an appropriately designed slow-light
set-up may simulate classical features of black holes -- such as horizon, mode
mixing, Bogoliubov coefficients, etc. -- it does not reproduce the related
quantum effects. PACS: 04.70.Dy, 04.80.-y, 42.50.Gy, 04.60.-m.Comment: 14 pages RevTeX, 5 figure
Gravity wave analogs of black holes
It is demonstrated that gravity waves of a flowing fluid in a shallow basin
can be used to simulate phenomena around black holes in the laboratory. Since
the speed of the gravity waves as well as their high-wavenumber dispersion
(subluminal vs. superluminal) can be adjusted easily by varying the height of
the fluid (and its surface tension) this scenario has certain advantages over
the sonic and dielectric black hole analogs, for example, although its use in
testing quantum effects is dubious. It can be used to investigate the various
classical instabilities associated with black (and white) holes experimentally,
including positive and negative norm mode mixing at horizons. PACS: 04.70.-s,
47.90.+a, 92.60.Dj, 04.80.-y.Comment: 14 pages RevTeX, 5 figures, section VI modifie
The Basics of Water Waves Theory for Analogue Gravity
This chapter gives an introduction to the connection between the physics of
water waves and analogue gravity. Only a basic knowledge of fluid mechanics is
assumed as a prerequisite.Comment: 36 pages. Lecture Notes for the IX SIGRAV School on "Analogue
Gravity", Como (Italy), May 201
Interplanetary and Geomagnetic Consequences of Interacting CMEs of 13-14 June 2012
We report on the kinematics of two interacting CMEs observed on 13 and 14
June 2012. Both CMEs originated from the same active region NOAA 11504. After
their launches which were separated by several hours, they were observed to
interact at a distance of 100 Rs from the Sun. The interaction led to a
moderate geomagnetic storm at the Earth with Dst index of approximately, -86
nT. The kinematics of the two CMEs is estimated using data from the Sun Earth
Connection Coronal and Heliospheric Investigation (SECCHI) onboard the Solar
Terrestrial Relations Observatory (STEREO). Assuming a head-on collision
scenario, we find that the collision is inelastic in nature. Further, the
signatures of their interaction are examined using the in situ observations
obtained by Wind and the Advance Composition Explorer (ACE) spacecraft. It is
also found that this interaction event led to the strongest sudden storm
commencement (SSC) (approximately 150 nT) of the present Solar Cycle 24. The
SSC was of long duration, approximately 20 hours. The role of interacting CMEs
in enhancing the geoeffectiveness is examined.Comment: 17 pages, 5 figures, Accepted in Solar Physics Journa
Free flux flow resistivity in strongly overdoped high-T_c cuprate; purely viscous motion of the vortices in semiclassical d-wave superconductor
We report the free flux flow (FFF) resistivity associated with a purely
viscous motion of the vortices in moderately clean d-wave superconductor
Bi:2201 in the strongly overdoped regime (T_c=16K) for a wide range of the
magnetic field in the vortex state. The FFF resistivity is obtained by
measuring the microwave surface impedance at different microwave frequencies.
It is found that the FFF resistivity is remarkably different from that of
conventional s-wave superconductors. At low fields (H<0.2H_c2) the FFF
resistivity increases linearly with H with a coefficient which is far larger
than that found in conventional s-wave superconductors. At higher fields, the
FFF resistivity increases in proportion to \sqrt H up to H_c2. Based on these
results, the energy dissipation mechanism associated with the viscous vortex
motion in "semiclassical" d-wave superconductors with gap nodes is discussed.
Two possible scenarios are put forth for these field dependence; the
enhancement of the quasiparticle relaxation rate and the reduction of the
number of the quasiparticles participating the energy dissipation in d-wave
vortex state.Comment: 9 pages 7 figures, to appear in Phys. Rev.
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