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Chemical Potential of Ideal Fermi and Bose Gases
Published in Kavati Venkateswarlu, Engineering Thermodynamics, 2020
The point at which phase transition takes place in case of an ideal gas of Bose atoms is dependent on temperature along the chemical potential. Chemical potential is zero at the transition point, and it continues to be so with a further decrease in temperature. And at this transition point, there appears a gas component with a macroscopically large number of particles called Bose–Einstein condensate (BEC) in one quantum-mechanical state identified by the lowest energy level of the system in the boson distribution function. In this distribution function, Bose-condensate component is mathematically described by a generalized function (Dirac delta function). All the gas particles must be in Bose-condensate state of zero temperature.
Bose-Einstein Condensate
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
Bose-Einstein condensate (BEC) is a state of matter in which all the neutral atoms or subatomic particles are cooled down to a temperature very near to absolute zero (i.e., 0 K). At such a low temperature, the thermal de-Broglie wavelength of the individual atoms starts overlapping with each other which results into the phase transition of the system such that a large number of bosons occupies the lowest energy level of the system or the lowest quantum state. In such a case, atoms can be illustrated by a single wave function on a near macroscopic scale. Thus, quantum effects become apparent on a macroscopic scale at the critical temperature which leads to macroscopic quantum phenomena.
Weakly nonlinear interactions of collective oscillations in a correlated degenerate fluid
Published in Waves in Random and Complex Media, 2022
In the case of high particle density , as we lower the temperature , the thermal de Broglie wavelength (, ℏ is Planck's constant and m is the mass) starts to be comparable to the inter-particle spacing . This is when the phase-space density and wave packets of different particles start to overlap with each other, leading to the quantum degeneracy. Under this circumstance, the wave-like nature (collective phenomena) becomes important and quantum effects must be taken into account. To investigate the collective processes, quantum hydrodynamic (QHD) model is developed from the well-known Wigner–Poisson equations (by taking the velocity moments of the Wigner phase-space distribution) [11–16]. The QHD have the same form as the classical NS hydrodynamic equations, which properly describe the collective dynamics of weakly interacting repulsive Bose gas in Bose–Einstein Condensate (BEC) [17], dense plasma [18–22] and also well explain the nonlinear collective dynamics of gravitating BEC [23]. All these QHD models are for weakly coupled degenerate fluid.
Dynamical synchronization of two Bosonic Josephson junctions induced by an external driving field in a double-cavity system
Published in Journal of Modern Optics, 2022
Perhaps the most experimentally explored synchronization phenomenon is in the superconducting Josephson junction. However, the superconducting Josephson junction can be simulated by a zero-temperature Bose-Einstein condensate in a double-potential well [19–22]. This simulated Josephson junction is called the Bosonic Josephson junction (BJJ). Our present paper focuses on how to control the dynamical synchronization of the two Bosonic Josephson junctions (BJJs). In the past two decades, the BJJ has been studied extensively. It is widely used to study the matter-wave interferometer [23,24], the generation of squeezing and entanglement [25–27], and so on. In a milestone work, Smerzi et al. discovered the existence of the Josephson oscillation (JO) regime and a new macroscopic quantum self-trapping (MQST) regime in BJJ [20]. This macroscopic quantum self-trapping phenomenon, which does not exist in the superconducting Josephson junction, is caused by the interaction between atoms in the BJJ [20]. This new phenomenon was subsequently verified experimentally [28]. The study of the JO regime and the MQST regime has now been extended to two-species BJJ [29–31]. Recently, P. Rosson et al. studied such a composite system of the interaction between the optical cavity and the Bosonic Josephson junction, and they found that photons in the cavity field can induce the MQST in the BJJ [32].
Pulse wave propagation in a deformable artery filled with blood: an analysis of the fifth-order mKdV equation with variable coefficients
Published in Waves in Random and Complex Media, 2021
Ying Yang, Feixue Song, Hongwei Yang
Since the first introduction of the soliton concept, the classical nonlinear evolution equations (NLEEs) which support soliton solutions, such as the Kortewe-de Vries (KdV) and the modified Korteweg-de Vries (mKdV) equations, which have been proposed to describe a variety of physical phenomena in the fields of hydrodynamics, elastic media, internal waves for certain special density stratifications, ocean dynamics, plasma physics, Bose-Einstein condensate (BEC), and so on. Compared with KdV equation, the derivation process of mKdV equation has certain difficulty and complexity, so it has certain research value. Compared with previous models describing solitary waves, the mKdV model can describe the interfacial waves in the two-layer liquid with gradually varying depth, which is more suitable for actual blood vascular system. In addition, the effect of the dispersion due to higher order derivative terms on solitons has been studied for the fifth order mKdV-type equation which are useful in the context of fluid mechanics.