Self-similar amplification in fiber Bragg gratings written in fiber amplifiers

We show, by using numerical simulations, that self-similar pulses with a duration on the order of few nanoseconds and an energy on the order of 10?μJ can be obtained at the output of a fiber Bragg grating (FBG) written in a fiber amplifier. The evolution of the amplified pulses is determined by the combined effect of Kerr nonlinearity, normal-dispersion, gain, and gain saturation, which limit the pulse energy. The output pulse mainly depends on the initial pulse energy rather than on the initial pulse profile. The reduced group velocity in FBGs can significantly increase the total gain for a given amplifier length. Hence we find that the proposed amplification scheme can be highly advantageous for amplification of nanosecond-scale pulses in fiber amplifiers.     

On d-Multiplicative Secret Sharing

A multiplicative secret sharing scheme allows players to multiply two secret-shared field elements by locally converting their shares of the two secrets into an additive sharing of their product. Multiplicative secret sharing serves as a central building block in protocols for secure multiparty computation (MPC). Motivated by open problems in the area of MPC, we introduce the more general notion of d-multiplicative secret sharing, allowing to locally multiply d shared secrets, and study the type of access structures for which such secret sharing schemes exist.     

Full counting statistics of a Luttinger liquid conductor

Nonequilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the time resolved full counting statistics of the transmitted charge is derived. It is given by the Fredholm determinant of the counting operator with a time-dependent scattering phase. The result has a form of counting statistics of noninteracting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the noninteracting leads.     

Nonequilibrium Luttinger liquid: zero-bias anomaly and dephasing

A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left and right movers yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling density of states.     

Towards a dephasing diode: asymmetric and geometric dephasing

We study the effect of a noisy environment on spin and charge transport in ballistic quantum wires with spin-orbit coupling (Rashba coupling). We find that the wire then acts as a dephasing diode, inducing very different dephasing of the spins of right and left movers. We also show how Berry phase (geometric phase) in a curved wire can induce such asymmetric dephasing, in addition to purely geometric dephasing. We propose ways to measure these effects through spin detectors, spin-echo techniques, and Aharanov-Bohm interferometry.     

Two-soliton interaction in the vicinity of a defect inside a fiber Bragg grating and its application for obtaining an all-optical memory

We study the interaction between two Bragg solitons in the vicinity of a defect inside a fiber Bragg grating. A soliton that is trapped in the defect can be released by launching a second soliton. The effect can be used to obtain an all-optical memory that is not strongly sensitive to the phase and the timing arrival of the solitons.     

Upper bound on the characters of the symmetric groups

Let C be a conjugacy class in the symmetric group S _n , and λ be a partition of n. Let f ^λ be the degree of the irreducible representation S ^λ , χ ^λ (C)– the character of S ^λ at C, and r ^λ (C)– the normalized character χ ^λ (C) f ^λ . We prove that there exist constants b > 0 and 1 > q > 0 such that for n > 4, for every conjugacy class C in S _n and every irreducible representation S ^λ of S _n ∣r ^λ (C)∣≦ ( max {q,λ ₁ n, λ ₁ ′ n}) ^{b ⋅ supp(C)} where supp (C) is the number of non-fixed digits under the action of a permutation in C, λ ₁ is the size of the largest part in λ, and λ ₁ ′ is the number of parts in λ. The proof is obtained by enumeration of rim hook tableaux, the Hook formula and probabilistic arguments. Combinatorial, algebraic and statistical applications follow this result. In particular, we estimate the rate of mixing of random walks on the alternating groups with respect to conjugacy classes. Oblatum 14-III-1995 & 30-X-1995     

The spectrum-generating groups program and the string

Schrödinger's approach was analytical, but it is equivalent to an algebraic treatment. We review the evolution of group theory as a physical tool and its application to the Hilbert space of Schrödinger's eigenstates. Special emphasis is put on recent results relating to the relativistic quantized string.Dedicated to the 100th anniversary of the birth of Erwin Schrödinger. Invited Lecture at the 1987 Washington APS Meeting, Symposium on Dynamical Symmetries.Also on leave from the Center for Particle Theory, University of Texas, Austin.     

Optimization of Adiabatic Selective Pulses

Adiabatic RF pulses play an important role in spin inversion due to their robust behavior in presence of inhomogeneous RF fields. These pulses are characterized by the trajectory swept by the tip of theB_effvector and the rate of motion upon it. In this paper, a method is described for optimizing adiabatic inversion pulses to achieve a frequency-selective magnetization inversion over a given bandwidth in a shorter time and to improve slice profile. An efficient adiabatic pulse is used as an initial condition. This pulse allows for flexibility in choosing its parameters; in particular, the transition sharpness may be traded off against the inverted bandwidth. The considerations for selecting the parameters of the pulse according to the requirements of the design are discussed. The optimization process then improves the slice profile by optimizing the rate of motion along the trajectory of the pulse while preserving the trajectory itself. The adiabatic behavior of the optimized pulses is fully preserved over a twofold range of variation in the RF amplitude which is sufficient for imaging applications in commercial high-field MRI machines. Design examples demonstrate the superiority of the optimized pulses over the conventional sech/tanh pulse.     

A Monte Carlo study of the Gross-Neveu model

Several lattice versions of the Gross-Neveu model are constructed and studied using Monte Carlo methods. The expected shiral structures are confirmed by the numerical results. The correct asymptotic freedom behaviour is recovered with the appropriate number of species taken into account. The models differ in their number of soft modes and their strong coupling behaviour. In some of them, chiral symmetry is restored at a finite coupling. The large-N, finite-temperature transition is also found in good agreement with the theoretical value.