Bose–Einstein condensation in geometrically deformed tubes

Exner, Pavel; Zagrebnov, Valentin A.

doi:10.1088/0305-4470/38/25/l01

Cited by 8 publications

(7 citation statements)

References 31 publications

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“…Similar phenomena should be also relevant for the performance of novel kinds of (cold) atom 10 , phonon 11 and laser waveguides 12 . Even more, the possibility of geometrically inducing confined states allows for the design of unused ways to create a Bose-Einstein condensate in a quasi-one dimensional Bose gas 13 . Last but not least, besides the possible practical applications, it should be noted that such systems constitute a very interesting theoretical framework for studying the correspondence between classical and quantum dynamics.…”

Section: Introductionmentioning

confidence: 99%

Bound states in open-coupled asymmetrical waveguides and quantum wires

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Rodríguez

Terrero-Escalante

2012

J. Phys. A: Math. Theor.

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The behavior of bound states in asymmetric cross, T and L shaped configurations is considered. Because of the symmetries of the wavefunctions, the analysis can be reduced to the case of an electron localized at the intersection of two orthogonal crossed wires of different width. Numerical calculations show that the fundamental mode of this system remains bound for the widths that we have been able to study directly; moreover, the extrapolation of the results obtained for finite widths suggests that this state remains bound even when the width of one arm becomes infinitesimal. We provide a qualitative argument which explains this behavior and that can be generalized to the lowest energy states in each symmetry class. In the case of odd-odd states of the cross we find that the lowest mode is bounded when the width of the two arms is the same and stays bound up to a critical value of the ratio between the widths; in the case of the even-odd states we find that the lowest mode is unbound up to a critical value of the ratio between the widths. Our qualitative arguments suggest that the bound state survives as the width of the vertical arm becomes infinitesimal.

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Section: Introductionmentioning

confidence: 99%

Bound states in open-coupled asymmetrical waveguides and quantum wires

Amore

Rodríguez

Terrero-Escalante

2012

J. Phys. A: Math. Theor.

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“…On the other hand, if q + (T , µ) approaches zero, the ground state harmonic density ρ 0 ω = ω d e q + 1−e q + may account for the condensate contribution to the total harmonic density ρ B ω (T , µ) when ω → 0. Recall that the bosonic quantities are defined only for q + (T , µ) 0 which follows from equation (12). d) is the Riemann zeta function, the ground state occupation vanishes in the thermodynamic limit.…”

Section: Bose-einstein Condensation Of Trapped Repulsive Bosons In D >mentioning

confidence: 99%

Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps

Myśliwy

Napiórkowski

2019

J. Stat. Mech.

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We discuss thermodynamic properties of harmonically trapped imperfect quantum gases. The spatial inhomogeneity of these systems imposes a redefinition of the mean-field interparticle potential energy as compared to the homogeneous case. In our approach, it takes the form a 2 N 2 ω d , where N is the number of particles, ω -the harmonic trap frequency, d -system's dimensionality, and a is a parameter characterizing the interparticle interaction. We provide arguments that this model corresponds to the limiting case of a long-ranged interparticle potential of vanishingly small amplitude. This conclusion is drawn from a computation similar to the well-known Kac scaling procedure, which is presented here in a form adapted to the case of an isotropic harmonic trap. We show that within our model, the imperfect gas of trapped repulsive bosons undergoes the Bose-Einstein condensation provided d > 1. The main result of our analysis is that in d = 1 the gas of attractive imperfect fermions with a = −a F < 0 is thermodynamically equivalent to the gas of repulsive bosons with a = a B > 0 provided the parameters a F and a B fulfill the relation a B + a F = . This result supplements similar recent conclusion about thermodynamic equivalence of two-dimensional uniform imperfect repulsive Bose and attractive Fermi gases.

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“…Theoretical studies of the motion of particles confined in branching planar stripes [16] or curved quantum wires have been the subject of intense theoretical research already for many years [17], [18], [19], [20], [21], [22], [23], [24]. It is well known, that inside an infinitely extended straight waveguide the propagation of a stationary mode along the tube axis is enabled only if the energy E of that mode is above a certain excitation threshold ε xt > 0, the precise value of ε xt depending on the geometric shape of the cross section of that waveguide.…”

Section: Introductionmentioning

confidence: 99%

“…has a vanishing contribution in the ground state, so that the Laplace operator becomes effectively two-dimensional. Theoretical studies on guided matter waves in branching waveguides often assume explicitely such a planar geometry connected to a two-dimensional Laplace operator ∂ 2 ∂x 2 + ∂ 2 ∂y 2 , for example [17], [18], [19], [20], [21], [22], [24], [27]. But a realistic thin film geometry cannot be described assuming a large thickness parameter w thickness (height) w z .…”

Section: Introductionmentioning

confidence: 99%

Cold Bose atoms around the crossing of quantum waveguides

Markowsky

Schopohl

2014

Phys. Rev. A

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We show that massive low energy particles traversing a branching zone or a crossing of quantum waveguides may experience a non standard trapping force that cannot be derived from a potential. For interacting cold Bose atoms we report on the formation of a localised Hartree ground state for three prototype waveguide geometries with broken translational symmetry: a cranked L-shaped waveguide L, a T -shaped waveguide T , and the crossing C of two quantum waveguides. The phenomenon is kinetic energy driven and cannot be described within the Thomas-Fermi approximation. Depending on the ratio κ (Γ) of joining lateral tube diameters of the respective waveguides Γ ∈ {C, L, T } delocalisation commences when the particle number N approaches a critical value N (Γ) c . For the case of a binary mixture of two different Bose atom species A and B we observe non standard trapping of both atom species for subcritical particle numbers. A sudden demixing quantum transition takes place as the total particle number N = NA + NB is increased at fixed mixing ratio NA/NB. Depending on the mass ratio mA/mB the heavier atom species delocalises first for a wide range of interaction parameters. The numerical calculations are based on a splitting scheme involving an analytic approximation to the short time asymptotics of the imaginary time quantum propagator of a single particle obeying to Dirichlet boundary conditions at the walls inside the respective waveguides.

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Bose–Einstein condensation in geometrically deformed tubes

Abstract: We show that Bose-Einstein condensate can be created in quasi-one-dimensional systems in a purely geometrical way, namely by bending or other suitable deformation of a tube.

Cited by 8 publications

References 31 publications

Bound states in open-coupled asymmetrical waveguides and quantum wires

Bound states in open-coupled asymmetrical waveguides and quantum wires

Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps

Cold Bose atoms around the crossing of quantum waveguides

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