arXiv subjects

Hadrien Kurkjian

Publications and source records attributed to Hadrien Kurkjian.

At least 19 recordsLinked to original sources

arXiv2026

A low-energy effective Hamiltonian for Landau quasiparticles: I. A unified theory of transport and superfluidity in Fermi liquids

We introduce a new renormalisation scheme to construct the Landau quasiparticles of Fermi fluids. The scheme introduces an energy cutoff $Λ$ to remove the resonant couplings, enabling the dressing of the particles into quasiparticles via a unitary transformation. The dynamics of the quasiparticles is then restricted to low-energy transitions and is fully determined by an effective Hamiltonian which unifies the Landau function $f$, the pair interaction $g$ responsible for superfluidity, and the collision amplitude $\mathcal{A}$ responsible for transport and equilibration. Studying the flow equation that results from infinitesimal variations of the cutoff, we recover the Bethe-Salpeter relation between $f$ and the forward limit of $\mathcal{A}$, and we demonstrate an analogue relation between $g$ and the frontal limit of $\mathcal{A}$. We show that our effective theory captures all the low-energy phenomena of Fermi liquids, from the equation of state to the transport properties, both in the normal and in the superfluid phase. We apply it to the calculation of non-Fermi liquid corrections to the quasiparticle lifetime. This publication is continued by arXiv:2607.07041 where we apply the effective theory to a Fermi fluid of ultracold atoms.

cond-mat.quant-gas↗

arXiv2026

A low-energy effective Hamiltonian for Landau quasiparticles: II Application to the contact Fermi gas

This article follows up on arxiv:2511.15938, in which we developed a new renormalization scheme to construct a quantized theory of Fermi liquids. Here, we apply this formalism to a low-temperature atomic Fermi gas where the short-range interactions are fully parametrized by the s-wave scattering length $a$. We benchmark our renormalized theory by recovering known perturbative results on the static properties of the Fermi gas, such as the Lee-Huang-Yang expansion of the equation of state, the Galitskii expansion of the momentum distribution, and the Gor'kov- Melik Barkhudarov preexponential correction to the critical temperature. We then turn to the transport dynamics and demonstrate the presence of a preexponential correction to the speed of zero sound when including corrections of second order in $a$. Finally, we develop an efficient numerical method to solve the transport equation exactly, and we apply to study the crossover from the collisionless to the hydrodynamic regime in the density and polarisation response functions.

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arXiv2026

The crossover from classical to quantum transport in a weakly-interacting Fermi gas

We present an exact solution of the quantum kinetic equation of a weakly interacting Fermi gas in the crossover from the degenerate Fermi-liquid regime to the classical Boltzmann gas. We construct families of orthogonal polynomials tailored to each angular momentum channel, enabling a fast and systematically improvable decomposition of the phase-space distribution. This approach yields accurate, non-variational predictions for the shear viscosity, thermal diffusivity, and spin diffusivity to leading order in the scattering length. We demonstrate that the commonly used relaxation-time approximation fails dramatically at low temperature--by up to 25%. Our method provides a numerically efficient framework for benchmarking transport in strongly correlated regimes and for simulating the kinetics of quantum gases beyond hydrodynamics.

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arXiv2025

Exact perturbative expansion of the transport coefficients of a normal low-temperature Fermi gas with contact interactions

We compute the shear viscosity, thermal conductivity and spin diffusivity of a Fermi gas with short-range interactions in the Fermi liquid regime of the normal phase, that is at temperatures $T$ much lower than the Fermi temperature $T_{\rm F}$ and much larger than the superfluid critical temperature $T_c$. Given recent advances in the precision of cold atom experiments, we provide exact results up to second-order in the interaction strength. We extend the Landau-Salpeter equation to compute the collision amplitude beyond the forward-scattering limit, covering all collisions on the Fermi surface. We treat the collision kernel exactly, leading to significant corrections beyond relaxation-time or variational approximations. The transport coefficients, as functions of the $s$-wave scattering length $a$ and Fermi wavenumber $k_{\rm F}$, follow $(1+γk_{\rm F}a)/a^2$ up to corrections of order $O(a^0)$, with a positive coefficient $γ$ for the viscosity and negative one for the thermal conductivity and spin diffusivity.

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arXiv2025

Dispersion of first sound in a weakly interacting ultracold Fermi liquid

At low temperature, a normal gas of unpaired spin-1/2 fermions is one of the cleanest realizations of a Fermi liquid. It is described by Landau's theory, where no phenomenological parameters are needed as the quasiparticle interaction function can be computed perturbatively in powers of the scattering length $a$, the sole parameter of the short-range interparticle interactions. Obtaining an accurate solution of the transport equation nevertheless requires a careful treatment of the collision kernel, {as the uncontrolled error made by the relaxation time approximations increases when the temperature $T$ drops below the Fermi temperature}. Here, we study sound waves in the hydrodynamic regime up to second order in the Chapman-Enskog's expansion. We find that the frequency $ω_q$ of the sound wave is shifted above its linear departure as $ω_q=c_1 q(1+αq^2τ^2)$ where $c_1$ and $q$ are the speed and wavenumber of the sound wave and the typical collision time $τ$ scales as $1/a^2T^2$. Besides the shear viscosity, the coefficient $α$ is described by a single second-order collision time which we compute exactly from an analytical solution of the transport equation, resulting in a positive dispersion $α>0$. Our results suggest that ultracold atomic Fermi gases are an ideal experimental system for quantitative tests of second-order hydrodynamics.

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arXiv2024

Emergence of Sound in a Tunable Fermi Fluid

Landau's Fermi-liquid (FL) theory has been successful at the phenomenological description of the normal phase of many different Fermi systems. Using a dilute atomic Fermi fluid with tunable interactions, we investigate the microscopic basis of Landau's theory with a system describable from first principles. We study transport properties of an interacting Fermi gas by measuring its density response to a periodic external perturbation. In an ideal Fermi gas, we measure for the first time the celebrated Lindhard function. As the system is brought from the collisionless to the hydrodynamic regime, we observe the emergence of sound, and find that the experimental observations are quantitatively understood with a first-principle transport equation for the FL. When the system is more strongly interacting, we find deviations from such predictions. Finally, we observe the shape of the quasiparticle excitations directly from momentum-space tomography and see how it evolves from the collisionless to the collisional regime. Our study establishes this system as a clean platform for studying Landau's theory of the FL and paves the way for extending the theory to more exotic conditions, such as nonlinear dynamics and FLs with strong correlations in versatile settings.

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arXiv2024

Probing pair correlations in Fermi gases with Ramsey-Bragg interferometry

We propose an interferometric method to probe pair correlations in a gas of spin-1/2 fermions. The method consists of a Ramsey sequence where both spin states of the Fermi gas are set in a superposition of a state at rest and a state with a large recoil velocity. The two-body density matrix is extracted via the fluctuations of the transferred fraction to the recoiled state. In the pair-condensed phase, the off-diagonal long-range order is directly reflected in the asymptotic behavior of the interferometric signal for long interrogation times. The method also allows to probe the spatial structure of the condensed pairs: the interferometric signal is an oscillating function of the interrogation time in the Bardeen-Cooper-Schrieffer regime; it becomes an overdamped function in the molecular Bose-Einstein condensate regime.

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arXiv2023

Interaction quenches in nonzero temperature fermionic condensates

We revisit the study of amplitude oscillations in a pair condensate of fermions after an interaction quench, and generalize it to nonzero temperature. For small variations of the order parameter, we show that the energy transfer during the quench determines both the asymptotic pseudo-equilibrated value of the order parameter and the magnitude of the oscillations, after multiplication by, respectively, the static response of the order parameter and spectral weight of the pair-breaking threshold. Since the energy transferred to the condensed pairs decreases with temperature as the superfluid contact, the oscillations eventually disappear at the critical temperature. For deeper quenches, we generalize the regimes of persistent oscillations and monotonic decay to nonzero temperatures, and explain how they become more abrupt and are more easily entered at high temperatures when the ratio of the initial to final gap either diverges, when quenching towards the normal phase, or tends to zero, when quenching towards the superfluid phase. Our results are directly relevant for existing and future experiments on the non-equilibrium evolution of Fermi superfluids near the phase transition.

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arXiv2022

Quasiparticle disintegration in fermionic superfluids

We study the fermionic quasiparticle spectrum in a zero-temperature superfluid Fermi gas, and in particular how it is modified by different disintegration processes. On top of the disintegration by emission of a collective boson ($1\to2$, subject of a previous study, PRL 124, 073404), we consider here disintegration events where three quasiparticles are emitted ($1\to3$). We show that both disintegration processes are described by a $t$-matrix self-energy (as well as some highly off-resonant vacuum processes), and we characterize the associated disintegration continua. At strong coupling, we show that the quasiparticle spectrum is heavily distorted near the $1\to3$ disintegration threshold. Near the dispersion minimum, where the quasiparticles remain well-defined, the main effect of the off-shell disintegration processes is to shift the location of the minimum by a value that corresponds to the Hartree shift in the BCS limit. With our approximation of the self-energy, the correction to the energy gap with respect to the mean-field result however remains small, in contrast with experimental measurements.

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arXiv2020

Collective excitation branch in the continuum of pair-condensed Fermi gases : analytical study and scaling laws

The pair-condensed unpolarized spin-$1/2$ Fermi gases have a collective excitation branch in their pair-breaking continuum (V.A. Andrianov, V.N. Popov, 1976). We study it at zero temperature, with the eigenenergy equation deduced from the linearized time-dependent BCS theory and extended analytically to the lower half complex plane through its branch cut, calculating both the dispersion relation and the spectral weights (quasiparticle residues) of the branch. In the case of BCS superconductors, so called because the effect of the ion lattice is replaced by a short-range electron-electron interaction, we also include the Coulomb interaction and we restrict ourselves to the weak coupling limit $Δ/μ\to 0^+$ ($Δ$ is the order parameter, $μ$ the chemical potential) and to wavenumbers $q=O(1/ξ)$ where $ξ$ is the size of a pair; when the complex energy $z_q$ is expressed in units of $Δ$ and $q$ in units of $1/ξ$, the branch follows a universal law insensitive to the Coulomb interaction. In the case of cold atoms in the BEC-BCS crossover, only a contact interaction remains, but the coupling strength $Δ/μ$ can take arbitrary values, and we study the branch at any wave number. At weak coupling, we predict three scales, that already mentioned $q\approx 1/ξ$, that $q\approx(Δ/μ)^{-1/3}/ξ$ where the real part of the dispersion relation has a minimum and that $q\approx (μ/Δ)/ξ\approx k_{\rm F}$ ($k_{\rm F}$ is the Fermi wave number) where the branch reaches the edge of its existence domain. Near the point where the chemical potential vanishes on the BCS side, $μ/Δ\to 0^+$, where $ξ\approx k_{\rm F}$, we find two scales $q\approx(μ/Δ)^{1/2}/ξ$ and $q\approx 1/ξ$. In all cases, the branch has a limit $2Δ$ and a quadratic start at $q=0$. These results were obtained for $μ>0$, where the eigenenergy equation admits at least two branch points $ε_a(q)$ and $ε_b(q)$ on the positive real axis, and for an analytic continuation through the interval $[ε_a(q),ε_b(q)] $. We find new continuum branches by performing the analytic continuation through $[ε_b(q),+\infty[$ or even, for $q$ low enough, where there is a third real positive branch point $ε_c(q)$, through $[ε_b(q),ε_c(q)]$ and $[ε_c(q),+\infty[$. On the BEC side $μ<0$ not previously studied, where there is only one real positive branch point $ ε_a(q)$, we also find new collective excitation branches under the branch cut $[ε_a (q),+\infty[$. For $μ>0$, some of these new branches have a low-wavenumber exotic hypoacoustic $z_q\approx q^{3/2}$ or hyperacoustic $z_q\approx q^{4/5}$ behavior. For $μ<0$, we find a hyperacoustic branch and a nonhypoacoustic branch, with a limit $2Δ$ and a purely real quadratic start at $q=0$ for $Δ/|μ|<0.222$.

cond-mat.quant-gas↗

arXiv2020

Absorption and emission of a collective excitation by a fermionic quasiparticle in a Fermi superfluid

We study the process of absorption or emission of a bosonic collective excitation by a fermionic quasiparticle in a superfluid of paired fermions. From the RPA equation of motion of the bosonic excitation annihilation operator, we obtain an expression of the coupling amplitude of this process which is limited neither to resonant processes nor to the long wavelength limit. We confirm our result by independently deriving it in the functional integral approach using the gaussian fluctuation approximation, and by comparing it in the long wavelength limit to the quantum hydrodynamic result. Last, we give a straightforward application of the coupling amplitude we obtain by calculating the lifetime of the bosonic excitations of arbitrary wave number. We find a mode quality factor that decreases from its maximum at low wave numbers and vanishes when the bosonic branch hits the pair-breaking continuum.

physics.atm-clus↗

arXiv2020

Damping of elementary excitations in one-dimensional dipolar Bose gases

In the presence of dipolar interactions the excitation spectrum of a Bose gas can acquire a local minimum. The corresponding quasiparticles are known as rotons. They are gaped and do not decay at zero temperature. Here we study the decay of rotons in one-dimensional Bose gases at low temperatures. It predominantly occurs due to the backscattering of thermal phonons on rotons. The resulting rate scales with the third power of temperature and is inversely proportional to the sixth power of the roton gap near the solidification phase transition. The hydrodynamic approach used here enables us to find the decay rate for quasiparticles at practically any momenta, with minimal assumptions on the exact form of the interparticle interactions. Our results are an essential prerequisite for the description of all the dissipative phenomena in dipolar gases and have direct experimental relevance.

cond-mat.quant-gas↗

arXiv2020

Beyond mean-field corrections to the quasiparticle spectrum of superfluid Fermi gases

We investigate the fermionic quasiparticle branch of superfluid Fermi gases in the BCS-BEC crossover and calculate the quasiparticle lifetime and energy shift due to its coupling with the collective mode. The only close-to-resonance process that low-energy quasiparticles can undergo at zero temperature is the emission of a bosonic excitation from the phononic branch. Close to the minimum of the branch we find that the quasiparticles remain undamped, allowing us to compute corrections to experimentally relevant quantities such as the energy gap, location of the minimum, effective mass, and Landau critical velocity.

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arXiv2019

Landau phonon-roton theory revisited for superfluid helium 4 and Fermi gases

Liquid helium and spin-1/2 cold-atom Fermi gases both exhibit in their superfluid phase two distinct types of excitations, gapless phonons and gapped rotons or fermionic pair-breaking excitations. In the long wavelength limit, revising and extending Landau and Khalatnikov's theory initially developed for helium [ZhETF 19, 637 (1949)], we obtain universal expressions for three- and four-body couplings among these two types of excitations. We calculate the corresponding phonon damping rates at low temperature and compare them to those of a pure phononic origin in high-pressure liquid helium and in strongly interacting Fermi gases, paving the way to experimental observations.

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arXiv2019

Pair-Breaking Collective Branch in BCS Superconductors and Superfluid Fermi Gases

We demonstrate the existence of a collective excitation branch in the pair-breaking continuum of superfluid Fermi gases and BCS superconductors. At zero temperature, we analytically continue the equation on the collective mode energy in Anderson's Random Phase Approximation or Gaussian fluctuations through its branch cut associated with the continuum, and obtain the full complex dispersion relation, including in the strong coupling regime. The branch exists as long as the chemical potential $μ$ is positive and the wave number below $\sqrt{2mμ}/\hbar$ (with m the fermion mass). In the long wavelength limit, the branch varies quadratically with the wave number, with a complex effective mass that we compute analytically for an arbitrary interaction strength.

cond-mat.quant-gas↗

arXiv2019

Prethermalization to thermalization crossover in a dilute Bose gas following an interaction ramp

The dynamics of a weakly interacting Bose gas at low temperatures is close to integrable due to the approximate quadratic nature of the many-body Hamiltonian. While the short-time physics after an abrupt ramp of the interaction constant is dominated by the integrable dynamics, integrability is broken at longer times by higher-order interaction terms in the Bogoliubov Hamiltonian, in particular by Beliaev-Landau scatterings involving three quasiparticles. The two-stage relaxation process is highlighted in the evolution of local observables such as the density-density correlation function: a dephasing mechanism leads the system to a prethermal stage, followed by true thermalization conveyed by quasiparticle collisions. Our results bring the crossover from prethermalization to thermalization within reach of current experiments with ultracold atomic gases.

cond-mat.quant-gas↗

arXiv2018

Transition from supersonic to subsonic waves in superfluid Fermi gases

We study the propagation of dispersive waves in superfluid Fermi gases in the BEC-BCS crossover. Unlike in other superfluid systems, where dispersive waves have already been studied and observed, Fermi gases can exhibit a subsonic dispersion relation for which the dispersive wave pattern appears at the tail of the wave front. We show that this property can be used to distinguish between a subsonic and a supersonic dispersion relation at unitarity.

cond-mat.quant-gas↗

arXiv2017

Three-phonon and four-phonon interaction processes in a pair-condensed Fermi gas

We study the interactions among phonons and the phonon lifetime in a pair-condensed Fermi gas in the BEC-BCS crossover in the collisionless regime. To compute the phonon-phonon coupling amplitudes we use a microscopic model based on a generalized BCS Ansatz including moving pairs, which allows for a systematic expansion around the mean field BCS approximation of the ground state. We show that the quantum hydrodynamic expression of the amplitudes obtained by Landau and Khalatnikov apply only on the energy shell, that is for resonant processes that conserve energy. The microscopic model yields the same excitation spectrum as the Random Phase Approximation, with a linear (phononic) start and a concavity at low wave number that changes from upwards to downwards in the BEC-BCS crossover. When the concavity of the dispersion relation is upwards at low wave number, the leading damping mechanism at low temperature is the Beliaev-Landau process 2 phonons $\leftrightarrow$ 1 phonon while, when the concavity is downwards, it is the Landau-Khalatnikov process 2 phonons $\leftrightarrow$ 2 phonons. In both cases, by rescaling the wave vectors to absorb the dependence on the interaction strength, we obtain a universal formula for the damping rate. This universal formula corrects and extends the original analytic results of Landau and Khalatnikov [ZhETF {\bf 19}, 637 (1949)] for the $2\leftrightarrow2$ processes in the downward concavity case. In the upward concavity case, for the Beliaev 1$\leftrightarrow$ 2 process for the unitary gas at zero temperature, we calculate the damping rate of an excitation with wave number $q$ including the first correction proportional to $q^7$ to the $q^5$ hydrodynamic prediction, which was never done before in a systematic way.

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