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233
Periodic Schrödinger Operators with Large Gaps and WannierStark Ladders
, 1994
"... smooth potentials (see, e.g., [2, 3, 4] and references therein). By a classical result, the spectrum of the one electron Schrodinger equation with periodic potential is in the form of bands and gaps. Recall that for smooth periodic potentials the size of the nth gap is rapidly decreasing and the ..."
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Cited by 38 (15 self)
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smooth potentials (see, e.g., [2, 3, 4] and references therein). By a classical result, the spectrum of the one electron Schrodinger equation with periodic potential is in the form of bands and gaps. Recall that for smooth periodic potentials the size of the nth gap is rapidly decreasing and the band widths increase linearly with the band index n (for more precise information see e.g. [5]). A common wisdom says that the KronigPenney model (made of a periodic array of Dirac delta functions) gives the slowest decay of gap widths. In this case the gap widths approach a constant at high energies and the gap to band ratio goes to zero like 1=n , with n the band index. So, in general, periodic potentials are expected to have a gap to band ratios that decrease at high energies at least as fast as 1=n . Periodic Schrodinger operators with singular interactions may have increasin
Neutrino masses and mixings from supersymmetry with bilinear Rparity violation: A theory for solar and atmospheric neutrino oscillations,” Phys
 Rev. D
, 2000
"... The simplest unified extension of the Minimal Supersymmetric Standard Model with bilinear R–Parity violation naturally predicts a hierarchical neutrino mass spectrum, in which one neutrino acquires mass by mixing with neutralinos, while the other two get mass radiatively. We have performed a full o ..."
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Cited by 22 (3 self)
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The simplest unified extension of the Minimal Supersymmetric Standard Model with bilinear R–Parity violation naturally predicts a hierarchical neutrino mass spectrum, in which one neutrino acquires mass by mixing with neutralinos, while the other two get mass radiatively. We have performed a full oneloop calculation of the neutralinoneutrino mass matrix in the bilinear Rp / MSSM, taking special care to achieve a manifestly gauge invariant calculation. Moreover we have performed the renormalization of the heaviest neutrino, needed in order to get meaningful results. The atmospheric mass scale and maximal mixing angle arise from treelevel physics, while solar neutrino scale and oscillations follow from calculable oneloop corrections. If universal supergravity assumptions are made on the softsupersymmetry breaking terms then the atmospheric scale is calculable as a function of a single Rp / violating parameter by the renormalization group evolution due to the nonzero bottom quark Yukawa coupling. The solar neutrino problem must be accounted for by the small mixing angle (SMA) MSW solution. If these assumptions are relaxed
A quantum fluctuation theorem
"... We consider a quantum system strongly driven by forces that are periodic in time. The theorem concerns the probability P(e) of observing a given energy change e after a number of cycles. If the system is thermostated by a (quantum) thermal bath, e is the total amount of energy transferred to the bat ..."
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Cited by 16 (0 self)
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We consider a quantum system strongly driven by forces that are periodic in time. The theorem concerns the probability P(e) of observing a given energy change e after a number of cycles. If the system is thermostated by a (quantum) thermal bath, e is the total amount of energy transferred to the bath, while for an isolated system e is the increase in energy of the system itself. Then, we show that P(e)/P(−e) = e βe, a parameterfree, modelindependent relation. In the past few years there has been a renewed interest in the study of quantum systems out of equilibrium, to a large extent stimulated by the design of new experimental settings and by the construction of new devices. If a system is well out of equilibrium, as for example when it is strongly driven by periodic forces, then linear response theory (understood as linear perturbations around the Gibbs measure) is insufficient. Even in the context of classical mechanics not many generic results are available beyond linear response. An interesting new development consists of a number of relations for strongly out of equilibrium systems, mainly regarding the distribution of work and entropy production. The first
Topological field theories and geometry of Batalin Vilkovisky algebras
 JHEP
"... The algebraic and geometric structures of deformations are analyzed concerning topological field theories of Schwarz type by means of the BatalinVilkovisky formalism. Deformations of the ChernSimonsBF theory in three dimensions induces the Courant algebroid structure on the target space as a sigm ..."
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Cited by 16 (2 self)
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The algebraic and geometric structures of deformations are analyzed concerning topological field theories of Schwarz type by means of the BatalinVilkovisky formalism. Deformations of the ChernSimonsBF theory in three dimensions induces the Courant algebroid structure on the target space as a sigma model. Deformations of BF theories in n dimensions are also analyzed. Two dimensional deformed BF theory induces the Poisson structure and three dimensional deformed BF theory induces the Courant algebroid structure on the target space as a sigma model. The deformations of BF theories in n dimensions induce the structures of BatalinVilkovisky algebras on the target space. 1
Chiral fermions and the standard model from the matrix model compactified on a torus, Prog
 Theor. Phys
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Modular invariant partition functions in the quantum Hall effect
"... We study the partition function for the lowenergy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard form of rational conformal field theories. In particular, it ..."
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Cited by 14 (3 self)
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We study the partition function for the lowenergy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard form of rational conformal field theories. In particular, it is invariant under modular transformations of the toroidal geometry made by the angular variable and the compact Euclidean time. The Jain series of plateaus have been described by two types of edge theories: the minimal models of the W1+∞ algebra of quantum areapreserving diffeomorphisms, and their nonminimal version, the theories with ̂ U(1) × ̂ SU(m) 1 affine algebra. We find modular invariant partition functions for the latter models. Moreover, we relate the Wen topological order to the modular transformations and the Verlinde fusion algebra. We find new, nondiagonal modular invariants which describe edge theories with extended symmetry algebra; their Hall conductivities match the experimental values beyond the Jain series.
Nilpotent Symmetries for a Spinning Relativistic Particle
 in Augmented Superfield Formalism, (Preprint hepth/0506109
"... Abstract: The local, covariant, continuous, anticommuting and nilpotent BecchiRouetStoraTyutin (BRST) and antiBRST symmetry transformations for all the fields of a (0 + 1)dimensional spinning relativistic particle are obtained in the framework of augmented superfield approach to BRST formalism. ..."
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Cited by 12 (3 self)
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Abstract: The local, covariant, continuous, anticommuting and nilpotent BecchiRouetStoraTyutin (BRST) and antiBRST symmetry transformations for all the fields of a (0 + 1)dimensional spinning relativistic particle are obtained in the framework of augmented superfield approach to BRST formalism. The trajectory of this superparticle is parametrized by a monotonically increasing parameter τ that is embedded in a Ddimensional flat Minkowski spacetime manifold. This physically useful onedimensional system is considered on a three (1 + 2)dimensional supermanifold which is parametrized by an even element τ and a couple of odd elements θ and ¯ θ of the Grassmann algebra. Two anticommuting sets of (anti)BRST symmetry transformations, corresponding to the underlying (super)gauge symmetries for the above system, are derived in the framework of augmented superfield formulation where (i) the horizontality condition, and (ii) the invariance of conserved quantities on the (super)manifolds play decisive roles. Geometrical interpretations for the above nilpotent symmetries (and their generators) are provided.
The universal, finite temperature, crossover functions of the quantum transition in the Ising chain in a transverse field, Nucl. Phys. B464
, 1996
"... We consider finite temperature properties of the Ising chain in a transverse field in the vicinity of its zero temperature, second order quantum phase transition. New universal crossover functions for static and dynamic correlators of the “spin ” operator are obtained. The static results follow from ..."
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We consider finite temperature properties of the Ising chain in a transverse field in the vicinity of its zero temperature, second order quantum phase transition. New universal crossover functions for static and dynamic correlators of the “spin ” operator are obtained. The static results follow from an early lattice computation of McCoy, and a method of analytic continuation in the space of coupling constants. The dynamic results are in the “renormalized classical ” region and follow from a proposed mapping of the quantum dynamics to the Glauber dynamics of a classical Ising chain. Typeset using REVTEX 1 I.
Electroweak baryogenesis in supersymmetric models,” Phys
 Rev. D
, 1996
"... The baryon density which may be produced during the electroweak phase transition in supersymmetric models is computed, taking into account the previously neglected effects of transport, strong and weak anomalous fermion number violation, thermal scattering, and a new method for computing CP violatin ..."
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The baryon density which may be produced during the electroweak phase transition in supersymmetric models is computed, taking into account the previously neglected effects of transport, strong and weak anomalous fermion number violation, thermal scattering, and a new method for computing CP violating processes during the transition. We can account for the observed baryon asymmetry, provided new CPviolating phases are greater than ∼ 10 −(2−4) , and some superpartners are light enough to be relevant during the transition, which takes place at a temperature of (50100) GeV. In one case, light superpartners are the top squarks and the charginos and/or the neutralinos; in another case the top squarks and both Higgs doublets are light. Our calculation is easily extended to the case of a general two Higgs model, where we find sufficient baryogenesis provided that a certain combination of parameters in the Higgs potential leads to a CP violating space dependent phase in the top quark mass of order 10 −3. 10/95 (revised version