Irreducible free energy expansion and overlaps locking in mean field spin glasses

We introduce a diagrammatic formulation for a cavity field expansion around the critical temperature. This approach allows us to obtain a theory for the overlap's fluctuations and, in particular, the linear part of the Ghirlanda-Guerra relationships (GG) (often called Aizenman-Contucci polynomials (AC)) in a very simple way. We show moreover how these constraints are "superimposed" by the symmetry of the model with respect to the restriction required by thermodynamic stability. Within this framework it is possible to expand the free energy in terms of these irreducible overlaps fluctuations and in a form that simply put in evidence how the complexity of the solution is related to the complexity of the entropy.Comment: 19 page

Chirality transfer and stereo-selectivity of imprinted cholesteric networks

Imprinting of cholesteric textures in a polymer network is a method of preserving a macroscopically chiral phase in a system with no molecular chirality. By modifying the elastics properties of the network, the resulting stored helical twist can be manipulated within a wide range since the imprinting efficiency depends on the balance between the elastics constants and twisting power at network formation. One spectacular property of phase chirality imprinting is the created ability of the network to adsorb preferentially one stereo-component from a racemic mixture. In this paper we explore this property of chirality transfer from a macroscopic to the molecular scale. In particular, we focus on the competition between the phase chirality and the local nematic order. We demonstrate that it is possible to control the subsequent release of chiral solvent component from the imprinting network and the reversibility of the stereo-selective swelling by racemic solvents

On the Microscopic Origin of Cholesteric Pitch

We present a microscopic analysis of the instability of the nematic phase to chirality when molecular chirality is introduced perturbatively. We show that previously neglected short-range biaxial correlations play a crucial role in determining the cholesteric pitch. We propose an order parameter which quantifies the chirality of a molecule.Comment: RevTeX 3.0, 4 pages, one included eps figure. Published versio

Probing molecular chirality by coherent optical absorption spectra

We propose an approach to sensitively probe the chirality of molecules by measuring their coherent optical absorption spectra. It is shown that quantum dynamics of the cyclic three-level chiral molecules driven by appropriately-designed external fields is total-phase dependent. This will result in chirality-dependent absorption spectra for the probe field. As a consequence, these absorption spectra can be utilized to identify molecular chirality and determinate enantiomer excess. The feasibility of the proposal with chiral molecules confined in hollow-core photonic crystal fiber (HC-PCF) is also discussed.Comment: 4 pages, 4 figure

Observation of a Chiral State in a Microwave Cavity

A microwave experiment has been realized to measure the phase difference of the oscillating electric field at two points inside the cavity. The technique has been applied to a dissipative resonator which exhibits a singularity -- called exceptional point -- in its eigenvalue and eigenvector spectrum. At the singularity, two modes coalesce with a phase difference of $\pi/2 .$ We conclude that the state excited at the singularity has a definitiv chirality.Comment: RevTex 4, 5 figure

Interdisciplinary Teaching and Research at a Liberal Arts College on Computational Biology

ABSTRACT This paper focuses in presenting several aspects of the interdisciplinary collaboration in teaching and research at a liberal arts college. In particular, it presents courses and research projects in the computational biology area, which naturally call for collaborative work between faculty members from mathematics & computer science and biology departments. It further discusses (1) challenges arising when doing interdisciplinary work, (2) the interaction between interdisciplinary teaching, research, and communication, (3) possible outcomes of such interdisciplinary training for both students and faculty members, and (4) how interdisciplinary training fits within the liberal arts philosophy