Leo Radzihovsky

We study the statistical mechanics of two-dimensional "super-Coulombic" plasmas, namely, neutral plasmas with power-law interactions longer ranged than Coulomb. To that end, we employ numerically exact large-scale Monte Carlo simulations. Contrary to naive energy-entropy arguments, we observe a charge confinement-deconfinement transition as a function of temperature. Remarkably, the transition lies in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. Our results corroborate recent dielectric medium and renormalization group calculations predicting effective long-scale Coulomb interactions in microscopically super-Coulombic gases. We explicitly showcase this novel dielectric screening phenomenon, capturing the emergent Coulomb potential and the associated crossover length scale. This is achieved by utilizing a new test charge based methodology for determining effective inter-particle interactions. Lastly, we show that this Coulomb emergence and the associated BKT transition occur universally across generic interactions and densities.

Motivated by recent experimental breakthroughs toward a realization of a solid-state Thorium-229 nuclear clock, we review the technology, basic physics motivation, and limitations of the present generation of atomic clocks. We then discuss prospects for a new generation of clocks based on an anomalous low-energy 8.4 eV nuclear transition in Th-229, with an extremely long lifetime of 641 seconds when doped into CaF crystals. To realize such solid-state nuclear clocks one must confront basic nuclear, AMO, and solid state physics questions. Key challenges are understanding and minimizing the effects of inhomogeneous broadening, associated with strains and electric field gradients due to both the Th dopants and intrinsic crystal defects.

Motivated to elucidate the nature of quantum phases and their criticality when entangled with a correlated quantum bath, we study interacting bosons on a "comb lattice"-a one-dimensional backbone (system) coupled at its sites to otherwise independent one-dimensional "teeth" chains (bath). We map out the corresponding phase diagram, detailing the nature of the phases and phase transitions. Controlled by the backbone and teeth hopping amplitudes, short-range interactions, and chemical potential, phases include a Mott insulator, backbone, and teeth Luttinger liquids and the long-range ordered incoherent superfluid. We explore their properties and potential realizations in condensed matter and cold-atom experiments and simulations.

We formulate a generalized D-dimensional field theory, parametrized by an O(d)×O(D) tensor field with an energetic longitudinal constraint, describing a new class of fluctuating "tattered" membranes, exhibiting a nonzero density of topological connectivity defects-slits, cracks, and faults at an effective medium level. For infinite-coupling constraint, the model reproduces the elastic membrane, with its rich anomalous elasticity realized by, e.g., graphene. Two additional fixed points emerge within the critical manifold: (i) globally attractive, "isotropic" O(d)×O(D), and (ii) "transverse," which in D=2 is the exact "dual" of the elastic membrane. Their properties are obtained in general D, d from the renormalization group and the self-consistent screening analyses. They correspond to critical points of an interesting class of constrained spin models.

Motivated by a number of realizations of long-range interacting systems, including ultracold atomic and molecular gases, we study a neutral plasma with power-law interactions longer ranged than Coulombic. We find that beyond a crossover length, such interactions are universally screened down to a standard Coulomb form in all spatial dimensions. This implies, counterintuitively, that in two dimensions and below, such a "super-Coulombic" gas is asymptotically Coulombically confining at low temperatures. At higher temperatures, the plasma undergoes a deconfining transition that in two dimensions is the same Kosterlitz-Thouless transition that occurs in a conventional Coulomb gas, but at an elevated temperature that we calculate. We also predict that, in contrast, above two dimensions, even when naively the bare potential is confining, there is no confined phase of the plasma at any nonzero temperature. In addition, the super-Coulomb to Coulomb crossover is followed at longer length scales by an unconventional "Debye-Huckel" screening, which leads to faster-than-Coulombic, power-law decay of the screened potential, in contrast to the usual exponentially decaying Yukawa potential. Furthermore, we show that power-law potentials that fall off more rapidly than Coulomb are screened down to a shorter-ranged power law rather than an exponential Debye-Huckel Yukawa form. We expect these prediction to be testable in simulations and hope they will inspire experimental studies in various platforms.

The twist-bend nematic liquid crystal phase is a three-dimensional fluid in which achiral bent molecules spontaneously form an orientationally ordered, macroscopically chiral, heliconical winding of a ten nanometer-scale pitch in the absence of positional ordering. Here, the structure of the twist-bend phase of the bent dimer CB7CB and its mixtures with 5CB is characterized, revealing a hidden invariance of the self-assembly of the twist-bend structure of CB7CB, such that over a wide range of concentrations and temperatures, the helix pitch and cone angle change as if the ground state for a pitch of the TB helix is an inextensible heliconical ribbon along the contour formed by following the local molecular long axis (the director). Remarkably, the distance along the length for a single turn of this helix is given by 2πR_mol, where R_mol is the radius of bend curvature of a single all-trans CB7CB molecule. This relationship emerges from frustrated steric packing due to the bent molecular shape: space in the fluid that is hard to fill attracts the most flexible molecular subcomponents, a theme of nanosegregation that generates self-assembled, oligomer-like correlations of interlocking bent molecules in the form of a brickwork-like tiling of pairs of molecular strands into duplex double-helical chains. At higher temperatures in the twist-bend phase, the cone angle is small, the director contour is nearly along the helix axis z, and the duplex chains are sequences of biaxial elements formed by overlapping half-molecule pairs, with an approximately 45° rotation of the biaxis between each such element along the chain.