1,027 research outputs found
Gapped Phases of Quantum Wires
We investigate possible nontrivial phases of a two-subband quantum wire. It
is found that inter- and intra-subband interactions may drive the electron
system of the wire into a gapped state. If the nominal electron densities in
the two subbands are sufficiently close to each other, then the leading
instability is the inter-subband charge-density wave (CDW). For large density
imbalance, the interaction in the inter-subband Cooper channel may lead to a
superconducting instability. The total charge-density mode, responsible for the
conductance of an ideal wire, always remains gapless, which enforces the
two-terminal conductance to be at the universal value of 2e^2/h per occupied
subband. On the contrary, the tunneling density of states (DOS) in the bulk of
the wire acquires a hard gap, above which the DOS has a non-universal
singularity. This singularity is weaker than the square-root divergency
characteristic for non-interacting quasiparticles near a gap edge due to the
"dressing" of massive modes by a gapless total charge density mode. The DOS for
tunneling into the end of a wire in a CDW-gapped state preserves the power-law
behavior due to the frustration the edge introduces into the CDW order. This
work is related to the vast literature on coupled 1D systems, and most of all,
on two-leg Hubbard ladders. Whenever possible, we give derivations of the
important results by other authors, adopted for the context of our study.Comment: 30 pages, 6 figures, to appear in "Interactions and Transport
Properties of Lower Dimensional Systems", Lecture Notes in Physics, Springe
Initial Conditions for Semiclassical Field Theory
Semiclassical approximation based on extracting a c-number classical
component from quantum field is widely used in the quantum field theory.
Semiclassical states are considered then as Gaussian wave packets in the
functional Schrodinger representation and as Gaussian vectors in the Fock
representation. We consider the problem of divergences and renormalization in
the semiclassical field theory in the Hamiltonian formulation. Although
divergences in quantum field theory are usually associated with loop Feynman
graphs, divergences in the Hamiltonian approach may arise even at the tree
level. For example, formally calculated probability of pair creation in the
leading order of the semiclassical expansion may be divergent. This observation
was interpretted as an argumentation for considering non-unitary evolution
transformations, as well as non-equivalent representations of canonical
commutation relations at different time moments. However, we show that this
difficulty can be overcomed without the assumption about non-unitary evolution.
We consider first the Schrodinger equation for the regularized field theory
with ultraviolet and infrared cutoffs. We study the problem of making a limit
to the local theory. To consider such a limit, one should impose not only the
requirement on the counterterms entering to the quantum Hamiltonian but also
the requirement on the initial state in the theory with cutoffs. We find such a
requirement in the leading order of the semiclassical expansion and show that
it is invariant under time evolution. This requirement is also presented as a
condition on the quadratic form entering to the Gaussian state.Comment: 20 pages, Plain TeX, one postscript figur
Exponentially Large Probabilities in Quantum Gravity
The problem of topology change transitions in quantum gravity is investigated
from the Wheeler-de Witt wave function point of view. It is argued that for all
theories allowing wormhole effects the wave function of the universe is
exponentially large. If the wormhole action is positive, one can try to
overcome this difficulty by redefinition of the inner product, while for the
case of negative wormhole action the more serious problems arise.Comment: 9 pages in LaTeX, 4 figures in PostScript, the brief version of this
paper is to appear in Proceedings of the XXIV ITEP Winter School of Physic
Semiclassical Description of Wavepacket Revival
We test the ability of semiclassical theory to describe quantitatively the
revival of quantum wavepackets --a long time phenomena-- in the one dimensional
quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are
considered: time-dependent WKB and Van Vleck propagation. We show that both
approaches describe with impressive accuracy the autocorrelation function and
wavefunction up to times longer than the revival time. Moreover, in the Van
Vleck approach, we can show analytically that the range of agreement extends to
arbitrary long times.Comment: 10 pages, 6 figure
Renormalization of Poincare Transformations in Hamiltonian Semiclassical Field Theory
Semiclassical Hamiltonian field theory is investigated from the axiomatic
point of view. A notion of a semiclassical state is introduced. An "elementary"
semiclassical state is specified by a set of classical field configuration and
quantum state in this external field. "Composed" semiclassical states viewed as
formal superpositions of "elementary" states are nontrivial only if the Maslov
isotropic condition is satisfied; the inner product of "composed" semiclassical
states is degenerate. The mathematical proof of Poincare invariance of
semiclassical field theory is obtained for "elementary" and "composed"
semiclassical states. The notion of semiclassical field is introduced; its
Poincare invariance is also mathematically proved.Comment: LaTeX, 40 pages; short version of hep-th/010307
On the Thermal Stability of Graphone
Molecular dynamics simulation is used to study thermally activated migration
of hydrogen atoms in graphone, a magnetic semiconductor formed of a graphene
monolayer with one side covered with hydrogen so that hydrogen atoms are
adsorbed on each other carbon atom only. The temperature dependence of the
characteristic time of disordering of graphone via hopping of hydrogen atoms to
neighboring carbon atoms is established directly. The activation energy of this
process is found to be Ea=(0.05+-0.01) eV. The small value of Ea points to
extremely low thermal stability of graphone, this being a serious handicap for
practical use of the material in nanoelectronics.Comment: 3 figure
Incoherent scatterer in a Luttinger liquid: a new paradigmatic limit
We address the problem of a Luttinger liquid with a scatterer that allows for
both coherent and incoherent scattering channels. The asymptotic behavior at
zero temperature is governed by a new stable fixed point: a Goldstone mode
dominates the low energy dynamics, leading to a universal behavior. This limit
is marked by equal probabilities for forward and backward scattering.
Notwithstanding this non-trivial scattering pattern, we find that the shot
noise as well as zero cross-current correlations vanish. We thus present a
paradigmatic picture of an impurity in the Luttinger model, alternative to the
Kane-Fisher picture.Comment: published version, 4 + epsilon pages, 1 figur
Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion
We explore dynamics of a density pulse induced by a local quench in a
one-dimensional electron system. The spectral curvature leads to an "overturn"
(population inversion) of the wave. We show that beyond this time the density
profile develops strong oscillations with a period much larger than the Fermi
wave length. The effect is studied first for the case of free fermions by means
of direct quantum simulations and via semiclassical analysis of the evolution
of Wigner function. We demonstrate then that the period of oscillations is
correctly reproduced by a hydrodynamic theory with an appropriate dispersive
term. Finally, we explore the effect of different types of electron-electron
interaction on the phenomenon. We show that sufficiently strong interaction
[ where is the fermionic mass and the relevant spatial
scale] determines the dominant dispersive term in the hydrodynamic equations.
Hydrodynamic theory reveals crucial dependence of the density evolution on the
relative sign of the interaction and the density perturbation.Comment: 20 pages, 13 figure
The quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the theory of heavy-light mesons
We construct a relativistic potential quark model of , , , and
mesons in which the light quark motion is described by the Dirac equation
with a scalar-vector interaction and the heavy quark is considered a local
source of the gluon field. The effective interquark interaction is described by
a combination of the perturbative one-gluon exchange potential
and the long-range Lorentz-scalar and
Lorentz-vector linear potentials and , where
. Within the quasiclassical approximation, we obtain
simple asymptotic formulas for the energy and mass spectra and for the mean
radii of , , , and mesons, which ensure a high accuracy of
calculations even for states with the radial quantum number . We
show that the fine structure of P-wave states in heavy-light mesons is
primarily sensitive to the choice of two parameters: the strong-coupling
constant and the coefficient of mixing of the long-range
scalar and vector potentials and .
The quasiclassical formulas for asymptotic coefficients of wave function at
zero and infinity are obtained.Comment: 22 pages, 6 figure
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