arXiv subjects

Shina Tan

Publications and source records attributed to Shina Tan.

36 records · Page 2Linked to original sources

arXiv2012

Directed-polymer systems explored via their quantum analogs: Topological constraints and their consequences

The equilibrium statistical mechanics of classical directed polymers in 2 dimensions is well known to be equivalent to the imaginary-time quantum dynamics of a 1+1-dimensional many-particle system, with polymer configurations corresponding to particle world-lines. This equivalence motivates the application of techniques originally designed for one-dimensional many-particle quantum systems to the exploration of many-polymer systems, as first recognized and exploited by P.-G. de Gennes [J.\ Chem.\ Phys.\ {\bf 48}, 2257 (1968)]. In this low-dimensional setting interactions give rise to an emergent polymer fluid, and we examine how topological constraints on this polymer fluid (e.g., due to uncrossable pins or barriers) and their geometry give rise to strong, entropy-driven forces. In the limit of large polymer densities, in which a type of mean-field theory is accurate, we find that a point-like pin causes a divergent pile-up of polymer density on the high-density side of the pin and a zero-density region (or gap) of finite area on the low-density. In addition, we find that the force acting on a pin that is only mildly displaced from its equilibrium position is sub-Hookean, growing less than linearly with the displacement, and that the gap created by the pin also grows sublinearly with the displacement. By contrast, the forces acting between multiple pins separated along the direction preferred by the polymers are super-Hookean. These nonlinear responses result from effective long-ranged interactions between polymer segments, which emerge via short-ranged interactions between distant segments of long polymer strands. In the present paper, we focus on the case of an infinitely strong, repulsive contact interaction, which ensures that the polymers completely avoid one another. In a companion paper, we consider the effects of a wider set of inter-polymer interactions.

cond-mat.soft↗

arXiv2011

Liberating Efimov physics from three dimensions

When two particles attract via a resonant short-range interaction, three particles always form an infinite tower of bound states characterized by a discrete scaling symmetry. It has been considered that this Efimov effect exists only in three dimensions. Here we review how the Efimov physics can be liberated from three dimensions by considering two-body and three-body interactions in mixed dimensions and four-body interaction in one dimension. In such new systems, intriguing phenomena appear, such as confinement-induced Efimov effect, Bose-Fermi crossover in Efimov spectrum, and formation of interlayer Efimov trimers. Some of them are observable in ultracold atom experiments and we believe that this study significantly broadens our horizons of universal Efimov physics.

cond-mat.quant-gas↗

arXiv2011

A Universal Energy Functional for Trapped Fermi Gases with Large Scattering Length

Yoram Alhassid conjectured that the total energy of a harmonically trapped two-component Fermi gas with large scattering length is a linear functional of the occupation probabilities of single-particle energy eigenstates. We confirm his conjecture and derive the functional explicitly. We show that the functional applies to ALL smooth potentials having a minimum, not just harmonic traps. We also calculate the occupation probabilities of high energy states.

cond-mat.quant-gas↗

arXiv2010

Confinement-induced p-wave resonances from s-wave interactions

We show that a purely s-wave interaction in three dimensions (3D) can induce higher partial-wave resonances in mixed dimensions. We develop two-body scattering theories in all three cases of 0D-3D, 1D-3D, and 2D-3D mixtures and determine the positions of higher partial-wave resonances in terms of the 3D s-wave scattering length assuming a harmonic confinement potential. We also compute the low-energy scattering parameters in the p-wave channel (scattering volume and effective momentum) that are necessary for the low-energy effective theory of the p-wave resonance. We point out that some of the resonances observed in the Florence group experiment [Phys. Rev. Lett. 104, 153202 (2010)] can be interpreted as the p-wave resonances in the 2D-3D mixed dimensions. Our study paves the way for a variety of physics, such as Anderson localization of matter waves under p-wave resonant scatterers.

cond-mat.quant-gas↗

arXiv2010

Relaxation of a high-energy quasiparticle in a one-dimensional Bose gas

We evaluate the relaxation rate of high-energy quasiparticles in a weakly interacting one-dimensional Bose gas. Unlike in higher dimensions, the rate is a nonmonotonic function of temperature, with a maximum at the crossover to the state of suppressed density fluctuations. At the maximum, the relaxation rate may significantly exceed its zero-temperature value. We also find the dependence of the differential inelastic scattering rate on the transferred energy. This rate yields information about temperature dependence of local pair correlations.

cond-mat.quant-gas↗

arXiv2009

Confinement-induced Efimov resonances in Fermi-Fermi mixtures

A Fermi-Fermi mixture of 40K and 6Li does not exhibit the Efimov effect in a free space, but the Efimov effect can be induced by confining only 40K in one dimension. Here the Efimov's three-body parameter is controlled by the confinement length. We show that the three-body recombination rate in such a system in the dilute limit has a characteristic logarithmic-periodic dependence on the effective scattering length with the scaling factor 22.0 and can be expressed by formulas similar to those for identical bosons in three dimensions. The ultracold mixture of 40K and 6Li in the 1D-3D mixed dimensions is thus a promising candidate to observe the Efimov physics in fermions.

cond-mat.other↗

arXiv2008

Universal Fermi gases in mixed dimensions

We investigate a two-species Fermi gas in which one species is confined in a two-dimensional plane (2D) or one-dimensional line (1D) while the other is free in the three-dimensional space (3D). We discuss the realization of such a system with the interspecies interaction tuned to resonance. When the mass ratio is in the range 0.0351<m_2D/m_3D<6.35 for the 2D-3D mixture or 0.00646<m_1D/m_3D<2.06 for the 1D-3D mixture, the resulting system is stable against the Efimov effect and has universal properties. We calculate key quantities in the many-body phase diagram. Other possible scale-invariant systems with short-range few-body interactions are also elucidated.

cond-mat.other↗

arXiv2008

Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas

For a two-component Fermi gas in the unitarity limit (ie, with infinite scattering length), there is a well-known virial theorem, first shown by J. E. Thomas et al, Phys. Rev. Lett. 95, 120402 (2005). A few people rederived this result, and extended it to few-body systems, but their results are all restricted to the unitarity limit. Here I show that there is a generalized virial theorem for FINITE scattering lengths. I also generalize an exact result concerning the pressure, first shown in cond-mat/0508320, to the case of imbalanced populations.

cond-mat.stat-mech↗

arXiv2008

Energetics of a strongly correlated Fermi gas

The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution: $$E_\text{internal}=\hbar^2ΩC/4πam+\sum_{\vect kσ}(\hbar^2 k^2/2m)(n_{\vect kσ}-C/k^4)$$ where the external potential energy is not included, $a$ is the scattering length, $Ω$ is the volume, $n_{\vect kσ}$ is the average number of fermions with wave vector $\vect k$ and spin $σ$, and $C\equiv\lim_{\vect k\to\infty} k^4 n_{\vect k\up} =\lim_{\vect k\to\infty} k^4 n_{\vect k\down}$. This result is a \textit{universal identity}. Its proof is facilitated by a novel mathematical idea, which might be of utility in dealing with ultraviolet divergences in quantum field theories. Other properties of this Fermi system, including the short-range structure of the one-body reduced density matrix and the pair correlation function, and the dimer-fermion scattering length, are also studied.

cond-mat.stat-mech↗

arXiv2008

Universal Fermi Gas with Two- and Three-Body Resonances

We consider a Fermi gas with two components of different masses, with the s-wave two-body interaction tuned to unitarity. In the range of mass ratio 8.62<M/m<13.6, it is possible for a single contact interaction between heavy fermions to produce a resonance in a three-body channel. The resulting system is scale invariant and has universal properties, and is very strongly interacting. When M/m is slightly above the lower limit 8.62, the ground state energy of a 2:1 mixture of heavy and light fermions is less than 2% of the energy of a noninteracting gas with the same number densities. We derive exact relationships between the pressures of the unitary Fermi gases with and without three-body resonance when the mass ratio is close to the critical values of 8.62 and 13.6. Possible experimental realization with cold atoms in optical lattices is discussed.

cond-mat.other↗

arXiv2007

Three-boson problem at low energy and Implications for dilute Bose-Einstein condensates

It is shown that the effective interaction strength of three bosons at small collision energies can be extracted from their wave function at zero energy. An asymptotic expansion of this wave function at large interparticle distances is derived, from which is defined a quantity $D$ named three-body scattering hypervolume, which is an analog of the two-body scattering length. Given any finite-range interaction potentials, one can thus predict the effective three-body force from a numerical solution of the Schrödinger equation. In this way the constant $D$ for hard-sphere bosons is computed, leading to the complete result for the ground state energy per particle of a dilute Bose-Einstein condensate (BEC) of hard spheres to order $ρ^2$, where $ρ$ is the number density. Effects of $D$ are also demonstrated in the three-body energy in a finite box of size $L$, which is expanded to the order $L^{-7}$, and in the three-body scattering amplitude in vacuum. Another key prediction is that there is a violation of the effective field theory (EFT) in the condensate fraction in dilute BECs, caused by short-range physics. EFT predictions for the ground state energy and few-body scattering amplitudes, however, are corroborated.

cond-mat.stat-mech↗

arXiv2006

A new many-body wave function for BCS-BEC crossover in Fermi gases

We present a new many body formalism for BCS-BEC crossover, which represents a modification of the BCS-Leggett ground state to include 4-fermion, and higher correlations. In the BEC regime, we show how our approach contains the \textit{Petrov et al} 4-fermion behavior and associated scattering length $a_{dd}$ at short distances, and secondly reduces to composite-boson Bogoliubov physics at long distances. It reproduces the Lee-Yang term, whose numerical value is also fixed by $a_{dd}$. We have also examined the next term beyond the Lee-Yang correction in a phenomenological fashion, building on cloud size data and collective mode experiments. However, one has to view this phenomenological analysis with some caution since experiments are in a state of flux and are performed close to unitarity.

cond-mat.stat-mech↗

arXiv2005

A new perturbation theory for the superfluid Fermi gas in the molecular Bose-Einstein condensed state

We demonstrate how solutions to quantum few-fermion scattering problems can be the point-of-departure of a new treatment of a generalized many-body wave function. Our focus is on a particular ansatz for the ground state wave function of a superfluid Fermi gas introduced earlier (cond-mat/0506293). Our method is perturbative in the sense that the probability amplitudes for few-fermion scattering processes are treated as small quantities; it is also NONPERTURBATIVE in the sense that whenever such scattering events occur, nonperturbative quantum few-fermion scattering physics dominates. This approach can be viewed as a new diagrammatic methodology, based on a wave function as distinct from a perturbation series in the interparticle interactions. Some generic properties of the wave function are studied, and its parameters in the Bose-Einstein condensed limit are computed beyond mean-field. These results enable us to predict many observable properties of this Fermi gas with well-controlled accuracy, such as the superfluid pairing function, the four-fermion and six-fermion correlation functions, the momentum distribution, and the two-body reduced density matrix, etc.

cond-mat.stat-mech↗

arXiv2005

Large momentum part of fermions with large scattering length

It is well known that the momentum distribution of the two-component Fermi gas with large scattering length has a tail proportional to $1/k^4$ at large $k$. We show that the magnitude of this tail is equal to the adiabatic derivative of the energy with respect to the reciprocal of the scattering length, multiplied by a simple constant. This result holds at any temperature (as long as the effective interaction radius is negligible) and any large scattering length; it also applies to few-body cases. We then show some more connections between the $1/k^4$ tail and various physical quantities, in particular the rate of change of energy in a DYNAMIC sweep of the inverse scattering length.

cond-mat.stat-mech↗

arXiv2005

S-wave contact interaction problem: A simple description

The s-wave contact interaction problem has a very simple structure and a simple and straightforward description. This is not a standard paper, and technicalities are avoided. A bare and simple picture of the problem is presented, in the hope that it will be helpful to our theoretical study of the problem.

cond-mat.stat-mech↗

arXiv2005

BCS-BEC Crossover: From High Temperature Superconductors to Ultracold Superfluids

We review the BCS to Bose Einstein condensation (BEC) crossover scenario which is based on the well known crossover generalization of the BCS ground state wavefunction $Ψ_0$. While this ground state has been summarized extensively in the literature, this Review is devoted to less widely discussed issues: understanding the effects of finite temperature, primarily below $T_c$, in a manner consistent with $Ψ_0$. Our emphasis is on the intersection of two important problems: high $T_c$ superconductivity and superfluidity in ultracold fermionic atomic gases. We address the "pseudogap state" in the copper oxide superconductors from the vantage point of a BCS-BEC crossover scenario, although there is no consensus on the applicability of this scheme to high $T_c$. We argue that it also provides a useful basis for studying atomic gases near the unitary scattering regime; they are most likely in the counterpart pseudogap phase. That is, superconductivity takes place out of a non-Fermi liquid state where preformed, metastable fermion pairs are present at the onset of their Bose condensation. As a microscopic basis for this work, we summarize a variety of $T$-matrix approaches, and assess their theoretical consistency. A close connection with conventional superconducting fluctuation theories is emphasized and exploited.

cond-mat.supr-con↗

arXiv2005

Short Range Scaling Laws of Quantum Gases With Contact Interactions

The probability amplitude for $N$ particles in a quantum gas with negligible range of interparticle interaction potentials to come to a small region of size $r$ scales like $r^γ$. It is shown that $γ$ is quantitatively related to the ground state energy of these $N$ fermions in the unitarity limit, confined by an isotropic harmonic potential. For large $N$, the short range density distribution of these $N$ particles is predominantly the same as the Thomas-Fermi profile of the gas in the unitarity limit confined by such a harmonic potential. These results may shed light on strongly interacting ultracold atomic Fermi gases, in a trap or on an optical lattice.

cond-mat.stat-mech↗

arXiv2004

Nernst Effect and Anomalous Transport in Cuprates: A Preformed-Pair Alternative to the Vortex Scenario

We address those puzzling experiments in underdoped high $T_c$ superconductors which have been associated with normal state "vortices" and show these data can be understood as deriving from preformed pairs with onset temperature $T^* > T_c$. For uncorrelated bosons in small magnetic fields, and arbitrary $T^*/T_c$, we present the exact contribution to \textit{all} transport coefficients. In the overdoped regime our results reduce to those of standard fluctuation theories ($T^*\approx T_c$). Semi-quantitative agreement with Nernst, ac conductivity and diamagnetic measurements is quite reasonable.

cond-mat.supr-con↗