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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Few-Boson Processes In The Presence Of An Attractive Impurity Under One-Dimensional Confinement, Nirav Mehta, Connor Morehead
Few-Boson Processes In The Presence Of An Attractive Impurity Under One-Dimensional Confinement, Nirav Mehta, Connor Morehead
Nirav P Mehta
We consider a few-boson system confined to one dimension with a single distinguishable particle of lesser mass. All particle interactions are modeled with δ functions, but due to the mass imbalance the problem is nonintegrable. Universal few-body binding energies, atom-dimer and atom-trimer scattering lengths, are all calculated in terms of two parameters, namely the mass ratio mL/mH, and ratio gHH/gHL of the δ-function couplings. We specifically identify the values of these ratios for which the atom-dimer or atom-trimer scattering lengths vanish or diverge. We identify regions in this parameter space in which various few-body inelastic processes become energetically allowed. In …
The Hyperspherical Four-Fermion Problem, Seth Rittenhouse, J Stecher, J D'Incao, Nirav Mehta, Chris Greene
The Hyperspherical Four-Fermion Problem, Seth Rittenhouse, J Stecher, J D'Incao, Nirav Mehta, Chris Greene
Nirav P Mehta
The problem of a few interacting fermions in quantum physics has sparked intense interest, particularly in recent years owing to connections with the behaviour of superconductors, fermionic superfluids and finite nuclei. This review addresses recent developments in the theoretical description of four fermions having finite-range interactions, stressing insights that have emerged from a hyperspherical coordinate perspective. The subject is complicated, so we have included many detailed formulae that will hopefully make these methods accessible to others interested in using them. The universality regime, where the dominant length scale in the problem is the two-body scattering length, is particularly stressed, including …
Born-Oppenheimer Study Of Two-Component Few-Particle Systems Under One-Dimensional Confinement, Nirav Mehta
Born-Oppenheimer Study Of Two-Component Few-Particle Systems Under One-Dimensional Confinement, Nirav Mehta
Nirav P Mehta
The energy spectrum, atom-dimer scattering length, and atom-trimer scattering length for systems of three and four ultracold atoms with δ-function interactions in one dimension are presented as a function of the relative mass ratio of the interacting atoms. The Born-Oppenheimer approach is used to treat three-body (“HHL”) systems of one light and two heavy atoms, as well as four-body (“HHHL”) systems of one light and three heavy atoms. Zero-range interactions of arbitrary strength are assumed between different atoms, but the heavy atoms are assumed to be noninteracting among themselves. Fermionic and bosonic heavy atoms with both positive and negative parity …
General Theoretical Description Of N-Body Recombination, Nirav Mehta, Seth Rittenhouse, J D’Incao, J Stecher, Chris Greene
General Theoretical Description Of N-Body Recombination, Nirav Mehta, Seth Rittenhouse, J D’Incao, J Stecher, Chris Greene
Nirav P Mehta
Formulas for the cross section and event rate constant describing recombination of N particles are derived in terms of general S-matrix elements. Our result immediately yields the generalized Wigner threshold scaling for the recombination of N bosons. A semianalytical formula encapsulates the overall scaling with energy and scattering length, as well as resonant modifications by the presence of N-body states near the threshold collision energy in the entrance channel. We then apply our model to the case of four-boson recombination into an Efimov trimer and a free atom.
Low-Energy Operators In Effective Theories, C Felline, Nirav Mehta, J Piekarewicz, James Shepard
Low-Energy Operators In Effective Theories, C Felline, Nirav Mehta, J Piekarewicz, James Shepard
Nirav P Mehta
Modern effective-theory techniques are applied to the nuclear many-body problem. A novel approach is proposed for the renormalization of operators in a manner consistent with the construction of the effective potential. To test this approach, a one-dimensional, yet realistic, nucleon-nucleon potential is introduced. An effective potential is then constructed by tuning its parameters to reproduce the exact effective-range expansion and a variety of bare operators are renormalized in a fashion compatible with this construction. Predictions for the expectation values of these effective operators in the ground state reproduce the results of the exact theory with remarkable accuracy (at the 0.5% …
Green’S Functions And The Adiabatic Hyperspherical Method, Seth Rittenhouse, Nirav Mehta, Chris Greene
Green’S Functions And The Adiabatic Hyperspherical Method, Seth Rittenhouse, Nirav Mehta, Chris Greene
Nirav P Mehta
We address the few-body problem using the adiabatic hyperspherical representation. A general form for the hyperangular Green’s function in d dimensions is derived. The resulting Lippmann-Schwinger equation is solved for the case of three particles with s-wave zero-range interactions. Identical particle symmetry is incorporated in a general and intuitive way. Complete semianalytic expressions for the nonadiabatic channel couplings are derived. Finally, a model to describe the atom loss due to three-body recombination for a three-component Fermi gas of Li6 atoms is presented.
Efimov States Embedded In The Three-Body Continuum, Nirav Mehta, Seth Rittenhouse, J D’Incao, Chris Greene
Efimov States Embedded In The Three-Body Continuum, Nirav Mehta, Seth Rittenhouse, J D’Incao, Chris Greene
Nirav P Mehta
We present analytical solutions for the three-body problem with multichannel interactions and identify a class of quasibound Efimov states that can be viewed as three-body Fano-Feshbach resonances. Our method employs a multichannel generalization of the Fermi pseudopotential to model low-energy atom-atom interactions near a magnetically tunable Fano-Feshbach resonance. We discuss the conditions under which quasibound Efimov states may be supported and identify the interaction parameters that limit the lifetimes of these states. We speculate that it may be possible to observe these states using spectroscopic methods, perhaps allowing for the measurement of multiple Efimov resonances.
Dimer-Dimer Collisions At Finite Energies In Two-Component Fermi Gases, J P. D'Incao, Seth T. Rittenhouse, Nirav P. Mehta, Chris H. Greene
Dimer-Dimer Collisions At Finite Energies In Two-Component Fermi Gases, J P. D'Incao, Seth T. Rittenhouse, Nirav P. Mehta, Chris H. Greene
Nirav P Mehta
We discuss a major theoretical generalization of existing techniques for handling the three-body problem that accurately describes the interactions among four fermionic atoms. Application to a two-component Fermi gas accurately determines dimer-dimer scattering parameters at finite energies and can give deeper insight into the corresponding many-body phenomena. To account for finite temperature effects, we calculate the energydependent complex dimer-dimer scattering length, which includes contributions from elastic and inelastic collisions. Our results indicate that strong finite-energy effects and dimer dissociation are crucial for understanding the physics in the strongly interacting regime for typical experimental conditions. While our results for dimer-dimer relaxation …
Three Bosons In One Dimension With Short-Range Interactions: Zero-Range Potentials, Nirav Mehta, James Shepard
Three Bosons In One Dimension With Short-Range Interactions: Zero-Range Potentials, Nirav Mehta, James Shepard
Nirav P Mehta
We consider the three-boson problem with δ-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the scattering of one free particle off a bound pair. We first follow a procedure outlined by McGuire in order to obtain an analytic expression for the desired S-matrix element. This result is then compared to a variational calculation in the adiabatic hyperspherical representation, and to a numerical solution to the momentum-space Faddeev equations. We find excellent agreement with the exact phase shifts, and comment on …
Three-Body Recombination In One Dimension, Nirav Mehta, B Esry, Chris Greene
Three-Body Recombination In One Dimension, Nirav Mehta, B Esry, Chris Greene
Nirav P Mehta
We study the three-body problem in one dimension for both zero- and finite-range interactions using the adiabatic hyperspherical approach. Particular emphasis is placed on the threshold laws for recombination, which are derived for all combinations of the parity and exchange symmetries. For bosons, we provide a numerical demonstration of several universal features that appear in the three-body system, and discuss how certain universal features in three dimensions are different in one dimension. We show that the probability for inelastic processes vanishes as the range of the pairwise interaction is taken to zero and demonstrate numerically that the recombination threshold law …