Effect of a finite number of particles in the Bose-Einstein condensation of a trapped gas

Napolitano, Reginaldo de Jesus; Luca, Jayme De; Bagnato, Vanderlei Salvador; Marques, G. C.

doi:10.1103/physreva.55.3954

Cited by 40 publications

(51 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…10(a) demonstrate. The cusp-like structure of the heat capacity that was predicted theoretically for a number of the confining potentials [35,36,[40][41][42][43] and observed experimentally for, e.g., the dilute Bose gas of 87 Rb atoms [44], for the infinite number of particles, N = ∞, turns at T = T cr into the discontinuity that is a manifestation of the phase transition; in our case, it is a transition from the BE condensate to the normal phase of the noninteracting particles in the linear potential. This justifies the definition of the critical temperature from Eq.…”

Section: Bosonsmentioning

confidence: 99%

“…[29]) reignited a huge interest in the topic [30][31][32][33]. Relevant to our research, let us mention a theoretical analysis of the influence of the different forms of the confining potential [30,[34][35][36][37][38][39] and/or BC [6][7][8][9][10][11][12][13][14][15][16][17][18] on the properties of the ideal Bose gas. A quantitative measure of the BE condensation is provided by the ground state occupation n 0 (E ; β), i.e., a ratio of the number of bosons N 0 in the ground state Table 1: Peak values of the specific heat per particle c N max and temperatures β −1 max at which they are achieved for the canonical and several numbers of particles N of the two grand canonical ensembles at some weak electric fields to the total number of corpuscles in the system:…”

Section: Bosonsmentioning

confidence: 99%

See 1 more Smart Citation

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

Olendski

2016

Annalen der Physik

View full text Add to dashboard Cite

A theoretical analysis of the thermodynamic properties of the Robin wall characterized by the extrapolation length Λ in the electric field E that pushes the particle to the surface is presented both in the canonical and two grand canonical representations and in the whole range of the Robin distance with the emphasis on its negative values which for the voltage-free configuration support negative-energy bound state. For the canonical ensemble, the heat capacity at Λ < 0 exhibits a nonmonotonic behavior as a function of the temperature T with its pronounced maximum unrestrictedly increasing for the decreasing fields as ln 2 E and its location being proportional to (− ln E ) −1 . For the Fermi-Dirac distribution, the specific heat per particle cN is a nonmonotonic function of the temperature too with the conspicuous extremum being preceded on the T axis by the plateau whose magnitude at the vanishing E is defined as 3(N − 1)/(2N )kB, with N being a number of the particles. The maximum of cN is the largest for N = 1 and, similar to the canonical ensemble, grows to infinity as the field goes to zero. For the Bose-Einstein ensemble, a formation of the sharp asymmetric feature on the cN -T dependence with the increase of N is shown to be more prominent at the lower voltages. This cusp-like dependence of the heat capacity on the temperature, which for the infinite number of bosons transforms into the discontinuity of cN (T ), is an indication of the phase transition to the condensate state. Some other physical characteristics such as the critical temperature Tcr and ground-level population of the Bose-Einstein condensate are calculated and analyzed as a function of the field and extrapolation length. Qualitative and quantitative explanation of these physical phenomena is based on the variation of the energy spectrum by the electric field.

show abstract

Section: Bosonsmentioning

confidence: 99%

Section: Bosonsmentioning

confidence: 99%

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

Olendski

2016

Annalen der Physik

View full text Add to dashboard Cite

show abstract

“…One can see a -type picture that resembles the corresponding result for liquid He (115). This qualitative aspect was found by different theories whether considering finite number effects (8,116) and interactions (117) or not (24).…”

Section: Global Heat Capacitymentioning

confidence: 53%

Quantum turbulence and thermodynamics on a trapped Bose-Einstein condensate

Shiozaki¹

View full text Add to dashboard Cite

In this thesis we have basically studied two aspects of Bose-Einstein condensation (BEC) in trapped dilute gases: (i) superfluidity with the possible onset of quantum turbulence (QT), and (ii) non-uniformity, which suggests the definition of new variables in order to build a global thermodynamic description. Both analyses were performed in a 87 Rb BEC magnetically trapped in a Quadrupole-Ioffe configuration (QUIC) trap. Concerning the first item, vortices and QT were generated by applying an oscillatory excitation formed by a quadrupole magnetic field superimposed onto the QUIC trapping potential. Scanning both the excitation amplitude and its duration allowed us to observe different regimes, particularly one with regular, well-defined vortices and another, where the onset of QT is believed to have occurred. The transition between this two regimes were explained by considering the finite-size characteristic of trapped gases. Additionally, data analyses on three vortex configurations suggested the presence of both vortices and antivortices (opposite circulation sign), and the vortex nucleation mechanism was proposed to be related to a relative motion between the condensate and thermal components, namely a counterflow. As for the second item, the BEC transition in our experiment was characterized in terms of new global thermodynamic variables. A phase diagram was constructed and compared to the superfluid helium phase transition. Finally, we provide preliminary results on the calculation of a global heat capacity, and briefly discuss the advantages of this new approach over the local density approximation alternative, particularly on BEC clouds in the presence of vortices and QT.

show abstract

“…In a harmonic trap, the energy spectrum is discrete and this assumption is not valid, particularly for small N at low energies. A correct treatment [5] shows that μdecreases slowly from its maximum value (equal to the ground-state energy) as T increases from zero, with the rate of decrease becoming suddenly rapid at some temperature close to the reference temperature T 0 c corresponding to the same value of N [4]. Thus, in this case, the critical temperature is not well defined.…”

Section: B Calculation Of Specific Heatmentioning

confidence: 95%

“…The features are markedly different from those of repulsive condensates, which are the only condensates that have been investigated so far. In a repulsive condensate, the heat capacity C N (T ) for a fixed number N of bosons in the trap, and also the critical temperature T c , smoothly approach a constant value * sg.phys.caluniv@gmail.com † tkdphy@caluniv.ac.in ‡ abc.anindya@gmail.com as N → ∞ [4,5]. As a function of T , the heat capacity for a given N increases to a maximum (C N ) max , then falls rapidly to a saturation value 3Nk B as T increases (k B is the Boltzmann constant).…”

Section: Introductionmentioning

confidence: 99%

Behavior of heat capacity of an attractive Bose-Einstein condensate approaching collapse

Goswami¹,

Das²,

Biswas³

2011

Phys. Rev. A

View full text Add to dashboard Cite

We report the calculation of heat capacity of an attractive Bose-Einstein condensate, with the number N of bosons increasing and eventually approaching the critical number N cr for collapse, using the correlated potential harmonics (CPH) method. Boson pairs interact via the realistic van der Waals potential. It is found that the transition temperature T c initially increases slowly, then rapidly as N becomes closer to N cr . The peak value of heat capacity for a fixed N increases slowly with N , for N far away from N cr . But after reaching a maximum, it starts decreasing when N approaches N cr . The effective potential calculated by the CPH method provides insight into this strange behavior.

show abstract

Effect of a finite number of particles in the Bose-Einstein condensation of a trapped gas

Cited by 40 publications

References 12 publications

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

Quantum turbulence and thermodynamics on a trapped Bose-Einstein condensate

Behavior of heat capacity of an attractive Bose-Einstein condensate approaching collapse

Contact Info

Product

Resources

About