3,920 research outputs found
Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
We study the quantum dynamics of a one-dimensional spin-1/2 anisotropic XY
model in a transverse field when the transverse field or the anisotropic
interaction is quenched at a slow but uniform rate. The two quenching schemes
are called transverse and anisotropic quenching respectively. Our emphasis in
this paper is on the anisotropic quenching scheme and we compare the results
with those of the other scheme. In the process of anisotropic quenching, the
system crosses all the quantum critical lines of the phase diagram where the
relaxation time diverges. The evolution is non-adiabatic in the time interval
when the parameters are close to their critical values, and is adiabatic
otherwise. The density of defects produced due to non-adiabatic transitions is
calculated by mapping the many-particle system to an equivalent Landau-Zener
problem and is generally found to vary as , where is the
characteristic time scale of quenching, a scenario that supports the
Kibble-Zurek mechanism. Interestingly, in the case of anisotropic quenching,
there exists an additional non-adiabatic transition, in comparison to the
transverse quenching case, with the corresponding probability peaking at an
incommensurate value of the wave vector. In the special case in which the
system passes through a multi-critical point, the defect density is found to
vary as . The von Neumann entropy of the final state is shown to
maximize at a quenching rate around which the ordering of the final state
changes from antiferromagnetic to ferromagnetic.Comment: 8 pages, 6 figure
Defect production due to quenching through a multicritical point
We study the generation of defects when a quantum spin system is quenched
through a multicritical point by changing a parameter of the Hamiltonian as
, where is the characteristic time scale of quenching. We argue
that when a quantum system is quenched across a multicritical point, the
density of defects () in the final state is not necessarily given by the
Kibble-Zurek scaling form , where is the
spatial dimension, and and are respectively the correlation length
and dynamical exponent associated with the quantum critical point. We propose a
generalized scaling form of the defect density given by , where the exponent determines the behavior of the
off-diagonal term of the Landau-Zener matrix at the multicritical
point. This scaling is valid not only at a multicritical point but also at an
ordinary critical point.Comment: 4 pages, 2 figures, updated references and added one figur
Defect generation in a spin-1/2 transverse XY chain under repeated quenching of the transverse field
We study the quenching dynamics of a one-dimensional spin-1/2 model in a
transverse field when the transverse field is quenched repeatedly
between and . A single passage from to or the other way around is referred to as a half-period of
quenching. For an even number of half-periods, the transverse field is brought
back to the initial value of ; in the case of an odd number of
half-periods, the dynamics is stopped at . The density of
defects produced due to the non-adiabatic transitions is calculated by mapping
the many-particle system to an equivalent Landau-Zener problem and is generally
found to vary as for large ; however, the magnitude is
found to depend on the number of half-periods of quenching. For two successive
half-periods, the defect density is found to decrease in comparison to a single
half-period, suggesting the existence of a corrective mechanism in the reverse
path. A similar behavior of the density of defects and the local entropy is
observed for repeated quenching. The defect density decays as
for large for any number of half-periods, and shows a increase in kink
density for small for an even number; the entropy shows qualitatively
the same behavior for any number of half-periods. The probability of
non-adiabatic transitions and the local entropy saturate to 1/2 and ,
respectively, for a large number of repeated quenching.Comment: 5 pages, 3 figure
How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?
Single centered supersymmetric black holes in four dimensions have
spherically symmetric horizon and hence carry zero angular momentum. This leads
to a specific sign of the helicity trace index associated with these black
holes. Since the latter are given by the Fourier expansion coefficients of
appropriate meromorphic modular forms of Sp(2,Z) or its subgroup, we are led to
a specific prediction for the signs of a subset of these Fourier coefficients
which represent contributions from single centered black holes only. We
explicitly test these predictions for the modular forms which compute the index
of quarter BPS black holes in heterotic string theory on T^6, as well as in Z_N
CHL models for N=2,3,5,7.Comment: LaTeX file, 17 pages, 1 figur
S-duality Action on Discrete T-duality Invariants
In heterotic string theory compactified on T^6, the T-duality orbits of dyons
of charge (Q,P) are characterized by O(6,22;R) invariants Q^2, P^2 and Q.P
together with a set of invariants of the discrete T-duality group O(6,22;Z). We
study the action of S-duality group on the discrete T-duality invariants and
study its consequence for the dyon degeneracy formula. In particular we find
that for dyons with torsion r, the degeneracy formula, expressed as a function
of Q^2, P^2 and Q.P, is required to be manifestly invariant under only a
subgroup of the S-duality group. This subgroup is isomorphic to \Gamma^0(r).
Our analysis also shows that for a given torsion r, all other discrete
T-duality invariants are characterized by the elements of the coset
SL(2,Z)/\Gamma^0(r).Comment: LaTeX file, 10 page
Small-world properties of the Indian Railway network
Structural properties of the Indian Railway network is studied in the light
of recent investigations of the scaling properties of different complex
networks. Stations are considered as `nodes' and an arbitrary pair of stations
is said to be connected by a `link' when at least one train stops at both
stations. Rigorous analysis of the existing data shows that the Indian Railway
network displays small-world properties. We define and estimate several other
quantities associated with this network.Comment: 5 pages, 7 figures. To be published in Phys. Rev.
Generalized Kac-Moody Algebras from CHL dyons
We provide evidence for the existence of a family of generalized
Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula
gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for
(N,k)=(1,10), (2,6), (3,4), and possibly (5,2). The square of the automorphic
form is the modular transform of the generating function of the degeneracy of
CHL dyons in asymmetric Z_N-orbifolds of the heterotic string compactified on
T^6. The new generalized Kac-Moody superalgebras all arise as different
`automorphic corrections' of the same Lie algebra and are closely related to a
generalized Kac-Moody superalgebra constructed by Gritsenko and Nikulin. The
automorphic forms, Delta_{k/2}(Z), arise as additive lifts of Jacobi forms of
(integral) weight k/2 and index 1/2. We note that the orbifolding acts on the
imaginary simple roots of the unorbifolded GKM superalgebra, G_1 leaving the
real simple roots untouched. We anticipate that these superalgebras will play a
role in understanding the `algebra of BPS states' in CHL compactifications.Comment: LaTeX, 35 pages; v2: improved referencing and discussion; typos
corrected; v3 [substantial revision] 44 pages, modularity of additive lift
proved, product representation of the forms also given; further references
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Scale-free network on a vertical plane
A scale-free network is grown in the Euclidean space with a global
directional bias. On a vertical plane, nodes are introduced at unit rate at
randomly selected points and a node is allowed to be connected only to the
subset of nodes which are below it using the attachment probability: . Our numerical results indicate that the directed
scale-free network for belongs to a different universality class
compared to the isotropic scale-free network. For the
degree distribution is stretched exponential in general which takes a pure
exponential form in the limit of . The link length
distribution is calculated analytically for all values of .Comment: 4 pages, 4 figure
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