arXiv subjects

Alan T. Dorsey

Publications and source records attributed to Alan T. Dorsey.

At least 19 recordsLinked to original sources

arXiv2026

Quantum geometry of the rotating shallow water model

The rotating shallow water equations (RSWE) are a mainstay of atmospheric and oceanic modeling, and their wave dynamics has close analogues in settings ranging from two-dimensional electron gases to active-matter fluids. While recent work has emphasized the topological character of RSWE wave bands, here we develop a complementary quantum-geometric description by computing the full quantum geometric tensor (QGT) for the linearized RSWE on an $f$-plane. The QGT unifies two pieces of band geometry: its real part defines a metric that quantifies how rapidly wave polarization changes with parameters, while its imaginary part is the Berry curvature that controls geometric phases and topological invariants. We obtain compact, symmetry-guided expressions for all three bands, highlighting the transverse structure of the metric and the monopole-like Berry curvature that yields Chern numbers for the Poincaré bands. Finally, we describe a feasible route to probing this geometry in rotating-tank experiments via weak, time-periodic parametric driving.

physics.flu-dyn↗

arXiv2024

Vortex dynamics in two-dimensional supersolids

We investigate the dynamics of quantized vortices in a model two-dimensional supersolid. Starting from an effective action that captures the dynamics of the superfluid condensate and its coupling to the lattice displacements, we integrate out the low-energy Goldstone modes-the phonons of the solid and the superfluid condensate-to arrive at an effective action for the vortices in the condensate. In the low-velocity limit we calculate the effective inertial mass for the vortices, and we find that the mass has a logarithmic frequency dependence, similar to the inertial mass found in superfluid vortices. The vortex dynamics also includes a Magnus force term in the equation of motion that arises from the Berry phase in the effective action.

cond-mat.quant-gas↗

arXiv2011

Dislocation-induced superfluidity in a model supersolid

Motivated by recent experiments on the supersolid behavior of $^4$He, we study the effect of an edge dislocation in promoting superfluidity in a Bose crystal. Using Landau theory, we couple the elastic strain field of the dislocation to the superfluid density, and use a linear analysis to show that superfluidity nucleates on the dislocation before occurring in the bulk of the solid. Moving beyond the linear analysis, we develop a systematic perturbation theory in the weakly nonlinear regime, and use this method to integrate out transverse degrees of freedom and derive a one-dimensional Landau equation for the superfluid order parameter. We then extend our analysis to a network of dislocation lines, and derive an XY model for the dislocation network by integrating over fluctuations in the order parameter. Our results show that the ordering temperature for the network has a sensitive dependence on the dislocation density, consistent with numerous experiments that find a clear connection between the sample quality and the supersolid response.

cond-mat.other↗

arXiv2010

Hydrodynamic theory of supersolids: Variational principle and effective Lagrangian

We develop an effective low-energy, long-wavelength theory of a bulk supersolid--a putative phase of matter with simultaneous crystallinity and Bose condensation. Using conservation laws and general symmetry arguments we derive an effective action that correctly describes the coupling between the Bose condensation and the elasticity of the solid. We use our effective action to calculate the correlation and response functions for the supersolid, and we show that the onset of supersolidity produces peaks in the response function, corresponding to propagating second sound modes in the solid. Throughout our work we make connections to existing work on effective theories of superfluids and normal solids, and we underscore the importance of conservation laws and symmetries in determining the number and character of the collective modes.

cond-mat.other↗

arXiv2009

Bound states of edge dislocations: The quantum dipole problem in two dimensions

We investigate bound state solutions of the 2D Schrödinger equation with a dipole potential originating from the elastic effects of a single edge dislocation. The knowledge of these states could be useful for understanding a wide variety of physical systems, including superfluid behavior along dislocations in solid $^4$He. We present a review of the results obtained by previous workers together with an improved variational estimate of the ground state energy. We then numerically solve the eigenvalue problem and calculate the energy spectrum. In our dimensionless units, we find a ground state energy of -0.139, which is lower than any previous estimate. We also make successful contact with the behavior of the energy spectrum as derived from semiclassical considerations.

cond-mat.other↗

arXiv2008

Viscoelastic Behavior of Solid $^4$He

Over the last five years several experimental groups have reported anomalies in the temperature dependence of the period and amplitude of a torsional oscillator containing solid $^4$He. We model these experiments by assuming that $^4$He is a viscoelastic solid--a solid with frequency dependent internal friction. We find that while our model can provide a quantitative account of the dissipation observed in the torsional oscillator experiments, it only accounts for about 10% of the observed period shift, leaving open the possibility that the remaining period shift is due to the onset of superfluidity in the sample.

cond-mat.other↗

arXiv2006

Anisotropic states of two-dimensional electrons in high magnetic fields

We study the collective states formed by two-dimensional electrons in Landau levels of index $n\ge 2$ near half-filling. By numerically solving the self-consistent Hartree-Fock (HF) equations for a set of oblique two-dimensional lattices, we find that the stripe state is an anisotropic Wigner crystal (AWC), and determine its precise structure for varying values of the filling factor. Calculating the elastic energy, we find that the shear modulus of the AWC is small but finite (nonzero) within the HF approximation. This implies, in particular, that the long-wavelength magnetophonon mode in the stripe state vanishes like $q^{3/2}$ as in an ordinary Wigner crystal, and not like $q^{5/2}$ as was found in previous studies where the energy of shear deformations was neglected.

cond-mat.mes-hall↗

arXiv2006

Static and dynamic properties of crystalline phases of two-dimensional electrons in a strong magnetic field

We study the cohesive energy and elastic properties as well as normal modes of the Wigner and bubble crystals of the two-dimensional electron system (2DES) in higher Landau levels. Using a simple Hartree-Fock approach, we show that the shear moduli ($c_{66}$'s) of these electronic crystals show a non-monotonic behavior as a function of the partial filling factor $ν^*$ at any given Landau level, with $c_{66}$ increasing for small values of $ν^*$, before reaching a maximum at some intermediate filling factor $ν^*_m$, and monotonically decreasing for $ν^*>ν^*_m$. We also go beyond previous treatments, and study how the phase diagram and elastic properties of electron solids are changed by the effects of screening by electrons in lower Landau levels, and by a finite thickness of the experimental sample. The implications of these results on microwave resonance experiments are briefly discussed.

cond-mat.mes-hall↗

arXiv2005

Squeezing superfluid from a stone: Coupling superfluidity and elasticity in a supersolid

In this work we start from the assumption that normal solid to supersolid (NS-SS) phase transition is continuous, and develop a phenomenological Landau theory of the transition in which superfluidity is coupled to the elasticity of the crystalline $^4$He lattice. We find that the elasticity does not affect the universal properties of the superfluid transition, so that in an unstressed crystal the well-known $λ$-anomaly in the heat capacity of the superfluid transition should also appear at the NS-SS transition. We also find that the onset of supersolidity leads to anomalies in the elastic constants near the transition; conversely, inhomogeneous strains in the lattice can induce local variations of the superfluid transition temperature, leading to a broadened transition.

cond-mat.soft↗

arXiv2003

Vortex Lattice Structural Transitions: a Ginzburg-Landau Model Approach

We analyze the rhombic to square vortex lattice phase transition in anisotropic superconductors using a variant of Ginzburg-Landau (GL) theory. The mean-field phase diagram is determined to second order in the anisotropy parameter, and shows a reorientation transition of the square vortex lattice with respect to the crystal lattice. We then derive the long-wavelength elastic moduli of the lattices, and use them to show that thermal fluctuations produce a reentrant rhombic to square lattice transition line, similar to recent studies which used a nonlocal London model.

cond-mat.supr-con↗

arXiv2003

Fingering of Electron Droplets in Nonuniform Magnetic Fields

A semiclassical analysis of a two-dimensional electron droplet in a high, nonuniform magnetic field predicts that the droplet will form ``fingered'' patterns upon increasing the number of electrons. We construct explicit examples of these patterns using methods first developed for the flow of two-dimensional viscous fluids. We complement our analytical results with Monte Carlo simulations of the droplet wavefunction, and find that at the point where the semiclassical analysis predicts a cusp on the interface, the droplet fissions--a type of ``quantum breakup'' phenomenon.

cond-mat.mes-hall↗

arXiv2001

Theory of Quantum Hall Nematics

Transport measurements on two dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally-ordered, compressible liquid state. We develop and analyze a microscopic theory of such a ``quantum Hall nematic'' (QHN) phase, predict the existence of a novel, highly anisotropic $q^3$ density-director mode, find that the T=0 long-range orientational order is unstable to weak disorder, and compute the tunneling into such a strongly correlated state. This microscopic approach is supported and complemented by a hydrodynamic model of the QHN, which, in the dissipationless limit, reproduces the modes of the microscopic model.

cond-mat.mes-hall↗

arXiv2001

Observability of quantum phase fluctuations in cuprate superconductors

We study the order parameter phase fluctuation effects in cuprate superconductors near T=0, using a quasi-two-dimensional d-wave BCS model. An effective phason theory is obtained which is used to estimate the strength of the fluctuations, the fluctuation correction to the in-plane penetration depth, and the pair-field susceptibility. We find that while the phase fluctuation effects are difficult to observe in the renormalization of the superfluid phase stiffness, they may be observed in a pair tunneling experiment which measures the pair-field susceptibility.

cond-mat.supr-con↗

arXiv2000

Disclination Unbinding Transition in Quantum Hall Liquid Crystals

We derive the the long-wavelength elastic theory for the quantum Hall smectic state starting from the Hartree-Fock approximation. Dislocations in this state lead to an effective nematic model for $T>0$, which undergoes a disclination unbinding transition from a phase with algebraic orientational order into an isotropic phase. We obtain transition temperatures which are in qualitative agreement with recent experiments which have observed large anisotropies of the longitudinal resistivities in half-filled Landau levels, lending credence to the liquid crystal interpretation of experiments.

cond-mat.mes-hall↗

arXiv1999

Physics on the edge: contour dynamics, waves and solitons in the quantum Hall effect

We present a theoretical study of the excitations on the edge of a two-dimensional electron system in a perpendicular magnetic field in terms of a contour dynamics formalism. In particular, we focus on edge excitations in the quantum Hall effect. Beyond the usual linear approximation, a non-linear analysis of the shape deformations of an incompressible droplet yields soliton solutions which correspond to shapes that propagate without distortion. A perturbative analysis is used and the results are compared to analogous systems, like vortex patches in ideal hydrodynamics. Under a local induction approximation we find that the contour dynamics is described by a non-linear partial differential equation for the curvature: the modified Korteweg-de Vries equation. PACS number(s): 73.40.Hm, 02.40.Ma, 03.40.Gc, 11.10.Lm

cond-mat.mes-hall↗

arXiv1999

Critical scaling of the a.c. conductivity for a superconductor above Tc

We consider the effects of critical superconducting fluctuations on the scaling of the linear a.c. conductivity, σ(ω), of a bulk superconductor slightly above Tc in zero applied magnetic field. The dynamic renormalization- group method is applied to the relaxational time-dependent Ginzburg-Landau model of superconductivity, with σ(ω) calculated via the Kubo formula to O(ε^{2}) in the ε= 4 - d expansion. The critical dynamics are governed by the relaxational XY-model renormalization-group fixed point. The scaling hypothesis σ(ω) \sim ξ^{2-d+z} S(ωξ^{z}) proposed by Fisher, Fisher and Huse is explicitly verified, with the dynamic exponent z \approx 2.015, the value expected for the d=3 relaxational XY-model. The universal scaling function S(y) is computed and shown to deviate only slightly from its Gaussian form, calculated earlier. The present theory is compared with experimental measurements of the a.c. conductivity of YBCO near Tc, and the implications of this theory for such experiments is discussed.

cond-mat.supr-con↗

arXiv1998

Solitons on the edge of a two-dimensional electron system

We present a study of the excitations of the edge of a two-dimensional electron droplet in a magnetic field in terms of a contour dynamics formalism. We find that, beyond the usual linear approximation, the non-linear analysis yields soliton solutions which correspond to uniformly rotating shapes. These modes are found from a perturbative treatment of a non-linear eigenvalue problem, and as solutions to a modified Korteweg-de Vries equation resulting from a local induction approximation to the nonlocal contour dynamics. We discuss applications to the edge modes in the quantum Hall effect.

cond-mat.mes-hall↗

arXiv1998

The effect of phase fluctuations on the single-particle properties of the underdoped cuprates

We study the effect of order parameter phase fluctuations on the single-particle properties of fermions in the underdoped cuprate superconductors using a phenomenological low-energy theory. We identify the fermion-phase field coupling as the Doppler-shift of the quasiparticle spectrum induced by the fluctuating superfluid velocity and we calculate the effect of these fluctuations on the fermion self-energy. We show that the vortex pair unbinding near the superconducting transition causes a significant broadening in the fermion spectral function, producing a pseudogap-like feature. We also discuss the specific heat and show that the phase fluctuation effect is visible due to the short coherence length.

cond-mat.supr-con↗