Leo Radzihovsky

Self-consistent theory of polymerized membranes

We study D-dimensional polymerized membranes embedded in d dimensions using a self-consistent screening approximation. It is exact for large d to order 1/d, for any d to order \ensuremath{\epsilon}=4-D, and for d=D. For flat physical membranes (D=2, d=3) it predicts a roughness exponent \ensuremath{\zeta}=0.590. For phantom membranes at the crumpling transition the size exponent is \ensuremath{\nu}=0.732. It yields identical lower critical dimension for the flat phase and crumpling transition

Theory of bent-core liquid-crystal phases and phase transitions.

{\mathit{D}}_{\mathrm{lc}}

BEC-BCS Crossover in 'Magnetized' Feshbach-Resonantly Paired Superfluids

(d)=2d/(d+1) (

Symmetries and elasticity of nematic gels.

{\mathit{D}}_{\mathrm{lc}}

Large- N expansion for unitary superfluid Fermi gases

= \ensuremath{\surd}2 for codimension 1). For physical membranes with random quenched curvature \ensuremath{\zeta}=0.775 in the new T=0 flat phase in good agremeent with simulations.

Nonequilibrium Dynamics and Thermodynamics of a Degenerate Fermi Gas Across a Feshbach Resonance

We study phases and phase transitions that can take place in the recently discovered bow-shaped or bent-core liquid-crystal molecules. We show that to completely characterize phases exhibited by such bent-core molecules a third-rank tensor T(ijk) order parameter is necessary in addition to the vector and the nematic (second-rank) tensor order parameters. We present an exhaustive list of possible liquid phases, characterizing them by their space-symmetry group and order parameters, and catalog the universality classes of the corresponding phase transitions that we expect to take place in such bent-core molecular liquid crystals. In addition to the conventional liquid-crystal phases such as the nematic phase, we predict the existence of other liquid phases, including the spontaneously chiral nematic (N(T)+2)(*) and chiral polar (V(T)+2)(*) phases, the orientationally ordered but optically isotropic tetrahedratic T phase, and a nematic N(T) phase with D(2d) symmetry that is neither uniaxial nor biaxial. Interestingly, the isotropic-tetrahedratic transition is continuous in mean-field theory, but is likely driven first order by thermal fluctuations. We conclude with a discussion of smectic analogs of these phases and their experimental signatures.

Resurrection of the melting line in the Bose glass superconductor.

We map out the detuning-magnetization phase diagram for a magnetized (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an s-wave Feshbach resonance (FR). The phase diagram is dominated by the coexistence of a magnetized normal gas and a singlet-paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced FR detuning. On the BCS side of strongly overlapping Cooper pairs, a sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized phase intervenes between the phase-separated and normal states. In contrast, for large negative detuning a uniform, polarized superfluid, that is, a coherent mixture of singlet Bose-Einstein-condensed molecules and fully magnetized single-species Fermi sea, is a stable ground state.

Quantum Liquid Crystals in an Imbalanced Fermi Gas: Fluctuations and Fractional Vortices in Larkin-Ovchinnikov States

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these materials.

Fluctuation-Driven 1st-Order Isotropic-to-Tetrahedratic Phase Transition

We analyze strongly interacting Fermi gases in the unitary regime by considering the generalization to an arbitrary number N of spin-1/2 fermion flavors with Sp(2N) symmetry. For N=\infty this problem is exactly solved by the BCS-BEC mean-field theory, with corrections small in the parameter 1/N. The large-N expansion provides a systematic way to determine corrections to mean-field predictions, allowing the calculation of a variety of thermodynamic quantities at (and in the proximity to) unitarity, including the energy, the pairing gap, and upper-critical polarization (in the case of a polarized gas) for the normal to superfluid instability. For the physical case of N=1, among other quantities, we predict in the unitarity regime, the energy of the gas to be \xi=0.28 times that for the non-interacting gas and the pairing gap to be 0.52 times the Fermi energy.

Critical transport in weakly disordered semiconductors and semimetals.

We consider a two-species degenerate Fermi gas coupled by a diatomic Feshbach resonance. We show that the resulting superfluid can exhibit a form of coherent BEC-to-BCS oscillations in response to a nonadiabatic change in the systems parameters, such as, for example, a sudden shift in the position of the Feshbach resonance. In the narrow resonance limit, the resulting solitonlike collisionless dynamics can be calculated analytically. In equilibrium, the thermodynamics can be accurately computed across the full range of BCS-BEC crossover, with corrections controlled by the ratio of the resonance width to the Fermi energy.