[Show abstract][Hide abstract] ABSTRACT: We present a systematic approach based on the multiple scattering formalism
due to Balian and Duplantier [Balian and Duplantier, Ann. Phys. (NY)
\textbf{104}, 300 (1977); \textbf{112}, 165 (1978)] for the calculation of the
Casimir interaction between arbitrarily shaped smooth conductors. The leading
two-point scattering term of the expansion has a simple compact form and for
many geometries captures the bulk of the interaction effect; it is an
improvement on the uncontrolled proximity force approximation which can be
extended to finite temperatures. The inclusion of terms beyond the two-point
approximation provides an accuracy check and reveals cases where the two-point
approximation is insufficient. We also analyze the anomalous situations
involving long cylindrical conductors where the two-point scattering
approximation fails. In such cases summation of the entire scattering series is
carried out and a topological argument is put forward as an explanation of the
result.
[Show abstract][Hide abstract] ABSTRACT: Surface electrons of strong topological insulator wires acquire a Berry phase
difference of $\pi$ on orbiting the wire. This can be detected in response of
clean wires (whose Fermi level is tuned to the Dirac point) to the presence of
the Aharonov-Bohm flux. Specifically, at half-odd integer applied flux (in
units of $hc/e$), long wires undergo semimetal-semiconductor transitions
characterized by logarithmically divergent susceptibility. Associated with
these are oscillations of magnetization (persistent current) that vanish both
at integer and half-odd integer flux. Additionally wires of arbitrary aspect
ratio exhibit conductance maxima at half-odd integer applied flux and minima at
integer flux. For long wires the maxima are sharp with their height approaching
$e^{2}/h$. Short wires are characterized by a universal conductivity $e^{2}/\pi
h$ attained in the disc limit.
[Show abstract][Hide abstract] ABSTRACT: We discuss the formalism of Balian and Duplantier [Balian and Duplantier, Ann. Phys. (NY) 104, 300 (1977); 112, 165 (1978)] for the calculation of the Casimir energy for an arbitrary smooth compact surface and use it to give some examples: a finite cylinder with hemispherical caps, a torus, an ellipsoid of revolution, a cube with rounded corners and edges, and a drum made of disks and part of a torus. We propose a model function that approximately captures the shape dependence of the Casimir energy.
Physical Review A 03/2014; 90(1). DOI:10.1103/PhysRevA.90.012514 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The field of charged impurities in narrow-band gap semiconductors and Weyl
semimetals can create electron-hole pairs when the total charge $Ze$ of the
impurity exceeds a value $Z_{c}e$. The particles of one charge escape to
infinity, leaving a screening space charge. The result is that the observable
dimensionless impurity charge $Q_{\infty}$ is less than $Z$ but greater than
$Z_{c}$. There is a corresponding effect for nuclei with $Z >Z_{c} \approx
170$, however in the condensed matter setting we find $Z_{c} \simeq 10$.
Thomas-Fermi theory indicates that $Q_{\infty} = 0$ for the Weyl semimetal, but
we argue that this is a defect of the theory. For the case of a highly-charged
recombination center in a narrow band-gap semiconductor (or of a supercharged
nucleus), the observable charge takes on a nearly universal value. In Weyl
semimetals the observable charge takes on the universal value $Q_{\infty} =
Z_{c}$ set by the reciprocal of material's fine structure constant.
Physical Review B 10/2013; 88(16). DOI:10.1103/PhysRevB.88.165428 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We calculate the increase in the number of modes (the Kac number) per unit length and the change in the zero-point energy (the Casimir energy) of the electromagnetic field resulting from the introduction of a thin, perfectly conducting cylindrical shell of elliptical cross section. Along the way we give a route to the calculation of these physical quantities. The Casimir energy is found to be attractive with the circular case corresponding to the energy maximum and the large eccentricity limit being the divergent energy minimum. As a result, with only Casimir stresses present, a fixed-area shell is unstable and might collapse onto itself. This instability is argued to persist at arbitrary temperature.
Physical Review A 02/2013; 87(2). DOI:10.1103/PhysRevA.87.022503 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A Coulomb impurity placed in an undoped Weyl semimetal spontaneously
surrounds itself with a cloud of condensed Weyl fermions. We find that the
ground-state of this system exhibits an experimentally accessible Landau
zero-charge effect: the fermion condensate completely screens out the impurity
charge. In a narrow band gap semiconducor this effect manifests itself in the
near universality of observable charge of a highly-charged recombination
center.
[Show abstract][Hide abstract] ABSTRACT: A Coulomb impurity placed in an undoped Weyl semimetal spontaneously
surrounds itself with a cloud of condensed Weyl fermions. We study this system
within the Thomas-Fermi approximation. We find that the ground-state of the
system is electrically neutral and exhibits an experimentally accessible Landau
zero-charge effect: the impurity charge is screened out at any finite distance
in the limit of vanishing impurity size. Specifically, we show how in this
limit the Thomas-Fermi equation for the electrostatic potential transforms into
the Gell-Mann-Low equation for the charge.
[Show abstract][Hide abstract] ABSTRACT: We compute the magnetic response of hollow semimetal cylinders and rings to
the presence of an axial Aharonov-Bohm magnetic flux, in the absence of
interactions. We predict nullification of the Aharonov-Bohm effect for a class
of dispersion laws that includes "non-relativistic" dispersion and demonstrate
that at zero flux the ground-state of a very short "armchair" graphene tube
will exhibit a ferromagnetic broken symmetry. We also compute the diamagnetic
response of bulk semimetals to the presence of a uniform magnetic field,
specifically predicting that the susceptibility has a logarithmic dependence on
the size of the sample.
[Show abstract][Hide abstract] ABSTRACT: A magnetic flux applied along the axis of a nanotube can counteract the
effect of the tube chirality and dramatically affect its conductance, leading
to a way to determine the chirality of a nanotube. The effect of the applied
flux is strongest in the long tube limit where the conductance is (i) either a
sequence of sharp $4e^{2}/h$ height peaks located at integer (in units of the
flux quantum) values of the flux (for an armchair tube) or (ii) a periodic
sequence of pairs of $2e^{2}/h$ height peaks for a chiral tube, with the
spacing determined by the chirality. In the short tube limit the conductance
takes on the value that gives the universal conductivity of an undoped graphene
sheet, with a small amplitude modulation periodic in the flux.
[Show abstract][Hide abstract] ABSTRACT: We compute the generic mode sum that quantifies the effect on the spectrum of
a harmonic field when a spherical shell is inserted into vacuum. This
encompasses a variety of problems including the Weyl spectral problem and the
Casimir effect of quantum electrodynamics. This allows us to resolve several
long-standing controversies regarding the question of universality of the
Casimir self-energy; the resolution comes naturally through the connection to
the Weyl problem. Specifically we demonstrate that in the case of a scalar
field obeying Dirichlet or Neumann boundary conditions on the shell surface the
Casimir self-energy is cutoff-dependent while in the case of the
electromagnetic field perturbed by a conductive shell the Casimir self-energy
is universal. We additionally show that an analog non-relativistic Casimir
effect due to zero-point magnons takes place when a non-magnetic spherical
shell is inserted inside a bulk ferromagnet.
Physical Review A 10/2011; 87(4). DOI:10.1103/PhysRevA.87.042519 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the energy spectrum for an aperiodic Josephson junction ladder, as a
function of frustration. Frustration is brought about by application of a
transverse magnetic field, and aperiodicity is imposed by the arrangement of
plaquettes with two incommensurate areas. We study the effect of the
incommensurate plaquette areas in conjunction with that of the aperiodicity.
The structure of the energy spectrum at deep minima is shown to be described by
a model that treats the plaquettes independently. The energy spectrum is a
quasiperiodic function of frustration; short range correlations in the
arrangement of plaquettes have a small effect on the energy power spectrum.
[Show abstract][Hide abstract] ABSTRACT: We study an array of inductively coupled Josephson junctions containing a single phase-slip site in the
presence of an alternating current. A phase-slip site with reduced critical current can serve as a permanent
source of solitary pulses which can synchronize the dynamics of an infinitely large array of junctions. We find that for definite values of parameters, increasing the coupling constant may prevent this synchronization in a system with periodic boundary conditions. This dependence on the boundary condition can be used as a coding mechanism and the information can be retrieved elsewhere in the array.
[Show abstract][Hide abstract] ABSTRACT: The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary we explore the relationship between such approaches, with the goal of better understanding the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and Candelas (1979), that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having geometrical origin, and an "intrinsic" term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff, and a non-geometrical intrinsic term. As by-products we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments. Comment: 13 pages, 1 figure, minor changes to the text, extra references added, version to be published in J. Phys. A
Journal of Physics A Mathematical and Theoretical 02/2010; 43(38). DOI:10.1088/1751-8113/43/38/385402 · 1.58 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate the origin of fractional Shapiro steps in arrays consisting of a few overdamped Josephson junctions. We show that when the symmetry reduces the equations to that of a single junction equation, only integer steps appear. Otherwise, fractional steps will appear when the evolution equations contain second (or higher) order derivatives or non-sinusoidal terms. We make a point of distinguishing the last two possibilities in the generation of the fractional steps.
[Show abstract][Hide abstract] ABSTRACT: Casimir forces are a manifestation of the change in the zero-point energy of the vacuum caused by the insertion of boundaries. We show how the Casimir force can be efficiently computed by consideration of the vacuum fluctuations that are suppressed by the boundaries, and rederive the scalar Casimir effects for a series of the Dirichlet geometries. For the planar case a finite universal force is automatically found. Consistent with other calculations of the effect, for curved geometries divergent (non-universal) expressions are encountered. They are interpreted geometrically following Candelas and Deutsch (1979) as largely due to the divergent self-energy of the boundary contributing to the force. This viewpoint is supported by explicit calculations for a wedge-circular arc geometry in two dimensions where non-universal and universal contributions into the effect can be unambiguously separated. We also give a heuristic derivation of the purely geometrical expression (Sen, 1981) for the non-universal piece of the Casimir energy due to an arbitrary smooth two-dimensional Dirichlet boundary of a compact region.
[Show abstract][Hide abstract] ABSTRACT: Casimir forces are a manifestation of the change in the zero-point energy of the vacuum caused by the insertion of boundaries. We show how the Casimir force can be computed by consideration of the vacuum fluctuations that are suppressed by the boundaries, and rederive the scalar Casimir effects for a series of geometries. For the planar case a finite universal force is automatically found. For curved geometries formally divergent expressions are encountered which we argue are largely due to the divergent self-energy of the boundary contributing to the force. This idea is supported by computing the effect for a fixed perimeter wedge-arc geometry in two dimensions.
[Show abstract][Hide abstract] ABSTRACT: We study the dynamics of a triangular single-plaquette Josephson-junction array in the development of the
fractional Shapiro steps. We show that synchronization on fractional steps can happen due to an intricate
interplay of the three junctions as the plaquette is made dynamically unsymmetric, either by applying an
external magnetic field or by changing the configuration of external currents. We propose a mechanism for
synchronization when the asymmetry is only due to the frustration induced by the magnetic field.
Physical Review B 12/2007; 76(21):214511. DOI:10.1103/PhysRevB.76.214511 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We compute an analog Casimir effect in a one-dimensional spinless Luttinger liquid confined to a segment in the presence of a nearly-impenetrable partition dividing the segment into two compartments. The Casimir interaction is found to be a bounded piecewise-continuous oscillatory function whose maxima are points of force discontinuity and correspond to resonant tunneling across the partition. The well-known regularization-based results are reproduced by the lower envelope of this function, which corresponds to an approximation that ignores the rather large oscillations due to particle discreteness. These macroscopic conclusions are tested and confirmed via a rigorous analysis of the Casimir effect in an exactly-solvable model of a one-dimensional non-relativistic spinless gas of free fermions, thus resolving an objection that has been raised by Volovik (2003). Additionally we confirm the result of a recent calculation which employed an effective low-energy theory with a cutoff to find the Casimir interaction between two strong well-separated impurities placed in a Luttinger liquid. Comment: 13 pages, 5 figures. A generalization to the case of an arbitrary harmonic liquid is given and discussion is improved. Version to be published in Phys. Rev. A
Physical Review A 06/2007; 78(2). DOI:10.1103/PhysRevA.78.022104 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We establish that the ability of a localized trapping potential to bind weakly-interacting bosons is dramatically enhanced in the vicinity of the threshold of formation of the single-particle bound-state of the trap. Specifically, for repulsive particles and a super-threshold trapping potential the equilibrium number of bound bosons and the size of the ground state diverge upon approaching the single-particle threshold from above. For attractive interactions and a sub-threshold trap a collective bound state always forms for a sufficiently large number of bosons despite the inability of interparticle attraction alone to form a two-body bound state. Comment: 6 pages, 3 figures. Minor changes, version to appear in PRA
Physical Review A 09/2006; 75(6). DOI:10.1103/PhysRevA.75.063421 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We discuss the implementation of two-photon emission and absorption in Cloudy, a general-purpose photoionization and radiative transfer code. We now include induced two-photon absorption between the 1s and 2s levels of hydrogen and hydrogen-like ions and between the 11S and 21S levels of the He-like isoelectronic sequence. We show sample calculations predicting the full emitted continuum and have implemented a method to allow this continuum to be saved in FITS format and reused in other applications.
Publications of the Astronomical Society of the Pacific 08/2006; 118(846):1176-1179. DOI:10.1086/506974 · 3.50 Impact Factor