Institute of Fundamental Technological Research

We analyze the three-dimensional (3D) buckling of an elastic filament in a shear flow of a viscous fluid at low Reynolds number and high Péclet number. We apply the Euler-Bernoulli beam (elastica) theoretical model. We show the universal character of the full 3D spectral problem for a small perturbation of a thin filament from a straight position of arbitrary orientation. We use the eigenvalues and eigenfunctions for the linearized elastica equation in the shear plane, found earlier by Liu et al. [Phys. Rev. Fluids 9, 014101 (2024)] with the Chebyshev spectral collocation method, to solve the full 3D eigenproblem. We provide a simple analytic approximation of the eigenfunctions, represented as Gaussian wave packets. As the main result of the paper, we derive the square-root dependence of the eigenfunction wave number on the parameter χ˜ = −η sin 2φ sin2 θ, where

We revisit the question concerning the stability of nonuniform superfluid states of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type to thermal and quantum fluctuations. On general grounds, we argue that the mean-field phase diagram hosting a Lifshitz point cannot be stable to fluctuations for isotropic, continuum systems, at any temperature T>0 in any dimensionality d<4. In contrast, in layered unidirectional systems, the lower critical dimension for the onset of FFLO-type long-range order accompanied by a Lifshitz point at T>0 is d=5/2. In consequence, its occurrence is excluded in d=2, but not in d=3. We propose a relatively simple method, based on nonperturbative renormalization group, to compute the critical exponents of the thermal m-axial Lifshitz point continuously varying m, spatial dimensionality d, and the number of order parameter components, N. We point out the possibility of a robust, fine-tuning free occurrence of a quantum Lifshitz point in the phase diagram of imbalanced Fermi mixtures.

We perform a detailed analysis of the phase transition between the uniform superfluid and normal phases in spin- and mass-imbalanced Fermi mixtures. At mean-field level we demonstrate that at temperature T→0 the gradient term in the effective action can be tuned to zero for experimentally relevant sets of parameters, thus providing an avenue to realize a quantum Lifshitz point. We subsequently analyze damping processes affecting the order-parameter field across the phase transition. We show that in the low-energy limit, Landau damping occurs only in the symmetry-broken phase and affects exclusively the longitudinal component of the order-parameter field. It is however unavoidably present in the immediate vicinity of the phase transition at temperature T=0. We subsequently perform a renormalization group analysis of the system in a situation, where, at mean-field level, the quantum phase transition is second order (and not multicritical). We find that, at T sufficiently low, including the Landau-damping term in a form derived from the microscopic action destabilizes the renormalization group flow toward the Wilson-Fisher fixed point. This signals a possible tendency to drive the transition weakly first order by the coupling between the order-parameter fluctuations and fermionic excitations effectively captured by the Landau-damping contribution to the order-parameter action.

We study the temporally nonlocal contributions to the gradient expansion of the pair fluctuation propagator for spin- and mass-imbalanced Fermi mixtures. These terms are related to the damping processes of soundlike (Anderson-Bogolyubov) collective modes and are relevant for the structure of the complex pole of the pair fluctuation propagator. We derive conditions under which damping occurs even at zero temperature for a large enough mismatch of the Fermi surfaces. We compare our analytical results with numerically computed damping rates of the Anderson-Bogolyubov mode.

We study the analytical structure of the effective action for spin- and mass-imbalanced Fermi mixtures at the onset of the superfluid state. Of our particular focus is the possibility of suppressing the tricritical temperature to zero, so that the transition remains continuous down to T  =  0 and the phase diagram hosts a quantum critical point. At mean-field level we analytically identify such a possibility in a regime of parameters in dimensionality d  =  3. In contrast, in d  =  2 we demonstrate that the occurrence of a quantum critical point is (at the mean-field level) excluded. We show that the Landau expansion of the effective potential remains well-defined in the limit except for a subset of model parameters which includes the standard BCS limit. We calculate the mean-field asymptotic shape of the transition line. Employing the functional renormalization group framework we go beyond the mean field theory and demonstrate the stability of the quantum critical point in d  =  3 with respect to fluctuations.

quantum phase transitions, quantum criticality, fermionic superfluids, renormalization group

Stokes equations, Euler-Bernoulli beam, elastica, elastic filament, shear flow, buckling