Questions tagged [bose-einstein-condensate]

A Bose–Einstein condensate is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero. In this state, a large fraction of the bosons occupy the *lowest quantum state* so that macroscopic quantum phenomena are in evidence. Use for all related BEC processes.

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Nonzero expectation value of boson creation operator in ground state of a Bose-Einstein condensate

I was following along with these notes, and just above equation (32) on page 3, the author makes the claim that, "for a Bose condensate, the ground state boson creation operator acquires a finite ...
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Why superfluid He-4 exhibits one degree of freedom zero viscosity but when for example rotated has a non-zero viscosity?

It is shown clearly in this demonstration that He-4 superfluid has zero viscosity for a one directional flow (i.e. one degree of freedom in motion) but shows viscous behavior when a more complex ...
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Composite fields and statistics

The usual explanation for superconductivity is that the electrons form Cooper pairs, which are bosons. This effective boson then condenses. E.g., quoting Wikipedia, Therefore, unlike electrons, ...
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How do we do experiments on gases at zero Kelvin?

We say that at temperatures very close to absolute zero (nano or pico Kelvin) there is no gas, so how do we do experiments on gases at zero Kelvin, and why is Bose-Einstein described as a gas? 1995 – ...
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How is a Bose-Einstein condensate produced from sodium atoms that do not have an integer spin?

In 1995 Wolfgang Ketterle at MIT produced a Bose-Einstein Condensate in a gas of sodium-23 atoms, but sodium-23 doesn't have an integer spin. How does this work?
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What is the difference between absolute zero Kelvin and almost absolute zero? [duplicate]

Scientists say that it is impossible to reach a temperature of zero kelvin, because the atoms will stop moving, and the volume of the substance will become zero, But we have reached the pico kelvin ...
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How the concept of "wave function of atom" in Bose-Einstein condensate should be interpreted from perspective of quantum field theory?

A typical description of Bose-Einstein condensate goes along the line of "multiple atoms in the same ground state can be described by the same wave function". But hold on. Atoms are not ...
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Is viscosity directly connected to non-superfluid component?

I am having questions when considering the microscopic models of superfluid BEC. In weakly interacting dilute alkali gas BECs, there are ways to introduce normal fluids without reducing the condensate ...
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Goldstone Modes, Galilean Symmetry, and Negative Excitations in Fermi Gas

Considering the centrality of Goldstone quasiparticles in condensed matter theories, I was wondering if the converse of the theorem might also be true: Does the existence of a gapless excitation imply ...
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Calculating the Feshbach resonances between carbon atoms

From my understanding, Feshbach resonance is a scattering resonance that occurs when the energy of an atom pair coincides with the energy of a molecular bound state. Feshbach resonances are ...
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Symmetry of momentum distribution in trapped BEC

Is the momentum distribution of excitations in a BEC symmetric? Even if there is a step potential (which I think should not make a difference because this is in real space)? I think yes, because ...
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Noether Charge in ideal fluid

I'm having some problems with the definition of the action in Euler fluid and in the Bose-Einstein condensate. In particular in this article https://arxiv.org/abs/1708.01526 the author apply the ...
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Bogoliubov-de Gennes equation and how to diagonalize

Can someone please share how you would go on to solve the Bogoliubov-de Gennes equation for a Bose-Einstein condensate with a potential. In particular, how would you deal with the diagonalization when ...
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Absorbing regions in Physics

How would you define an absorbing region (at the walls of a finite numerical simulation) in physics and how would you implement it? Can it be simulated by a high potential, low negative potential at ...
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Bogoliubov-de Gennes equation

Can we still assume translational invariance, and thus plane wave solutions, for the Bogoliubov-de Gennes equation for a trapped Bose-Einstein condensate (e.g., step or harmonic)?
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How does all of the superfluid empty from the beaker?

From what I understand, a superfluid is comprised of its normal fluid component and superfluid component (Landau's two fluid model). This normal fluid component has viscosity. What I don't understand, ...
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Is it a prerequisite for the usage of the Gross-Pitaevskii equation, to assume a dilute Bose gas?

Is it a prerequisite for the usage of the Gross-Pitaevskii equation, to assume a dilute Bose gas? Or is it also for Bose-Einstein condensates which are not so dilute?
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Phonons are bosons, but still we apply Maxwell distribution in einstein model. Why?

Phonons are bosons, but still we apply Maxwell distribution in the no.of oscillator while calculating the total energy and specific heat from it in the Einstein model, can anyone explain why?
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Heisenberg's uncertainty principle in frames of reference with different velocities

The Heisenberg's uncertainty principle \begin{align}\Delta x \Delta p \geq \frac{\hbar}{2},\end{align} states that two canonically conjugate variables can't be measured simultaneously with arbitrary ...
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What is the (kinetic) energy range of a particle in Bose condensate?

Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.67 °F). In ...
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Particle density vs. Probability Density in Quantum Mechanics

I am currently reading trough "Bose-Einstein Condensation and Superfluidity" by Pitaevksii and Stringari and noticed some inconsistencies in my reasoning. In Chapter 5 (Non-uniform Bose ...
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Interpretation of the Bose-Einstein Condensate Wavefunction squared and Density Matrix

I'm currently trying to get some background information about the theoretical treatment of Bose-Einstein Condensate, and I'm reading through this paper on the topic by J. Rogel Salazar. I have also ...
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Is vortex physics key to understand the universe simulation hypothesis? [duplicate]

Seth Lloyd, US computer scientist and Professor of Mechanical Engineering and Physics at the renowned Massachusetts Institute of Technology (MIT) says that the universe itself is a giant quantum ...
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Under what conditions is the Bose-Einstein distribution approximated by the Maxwell-Boltzmann distribution?

I am reading the book "C. J. Pethick, H. Smith - Bose-Einstein condensation in dilute gases". It says the Bose-Einstein distribution function is: $$f(E) = \frac{1}{e^{\frac{E-\mu}{kT}} - 1}$$...
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Minimizing Free Energy when considering multiple particles

I am reading an article about Gross-Pitaevskii Equation using a variational method approach. I am confused about a step of the derivation of free energy. We want to minimize:$$F=E-\mu N$$ and $$E(\psi)...
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Phase space density for Bose-Einstein condensation

A figure of merit for Bose-Einstein condensation is the phase space density which can be defined as $$\rho=n\lambda_T^3,$$ where $n$ is the number density of atoms and $\lambda_T$ the thermal de ...
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Can a Bose-Einstein condensate be made of any boson?

Can a Bose-Einstein condensate be made of any boson, or even two different types of bosons. Since none have to obey the Pauli exclusion principle, if so, how can we predict how one would like?
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Why at high energies, Fermi-Dirac and Bose-Einstein distribution behaves as Maxwell-Boltzman distribution? What is the physical explanantion?

I was searching for the reason that why at higher energies, the FD and BE distributions behave as MB distribution. In Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles by Eisberg and ...
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Could the rotating superfluid halo around a galaxy form a regular Abrikosov vortex lattice and serve as a naturally generated Quantum Matrix?

Spherical halo (shown in blue) surrounding galaxies could be a superfluid [Bose-Einstein condensate] according to Prof. Justin Khoury's hypothesis and may help to understand dark matter and galactic ...
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Is it correct to use mean-field Gross–Pitaevskii equation to study the internal dynamics of neutron star?

I'm putting this question because as I heard neutron stars are very dense entities. But one of the criteria to apply mean-field Gross-Pitaevskii(GPE) model is that the system should obey diluteness (...
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Could the universe behave like a Bose-Einstein condensate in the distant future?

Question: If the universe keeps expanding and getting cooler, and the temperature asymptotically approaches absolute zero over time... Could the universe behave like a Bose-Einstein condensate in the ...
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Single particle density of states for non-free particle

I am trying to find the single particle density of states in terms of the energy, for a system with the single particle 2D Hamiltonian: $$H=\frac{p^2}{2 m}+\alpha x \text { with } 0<y<L, x>0$$...
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What is the correct definition of the fermionic condensate?

I read that fermionic atoms could transit between a BEC-molecular and a BCS-pair state depending on the interaction strength. Since the process is a cross-over and changes are continuous over two ...
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Gross-Pitaevskii Equation regarding

Sir, I have been studying the Gross-Pitaevskii equation for weakly interacting Bose gas and I want to find out the Green's function for the equation: $$i\hbar\frac{\partial}{\partial t}\psi(r,t)=\Big[-...
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Connection between superfluidity and temperature

I don't understand the significance of temperature in relation to the presence of superfluidity. Why, in general, are low temperatures necessary?
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Is a vortex crystal a supersolid?

Reading the article [Rev. Mod. Phys. 84, 759 (2012)] by Prokof'ev and Boninsegni, a supersolid is defined as a homogeneous phase of matter in which both density long-range order (i.e. ordered spatial ...
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How to calculate scattering length for system with particles with different lengths

I am confused by the concepet of scattering length and how to calculate it. Suppose we have a system whose Hamiltonian is: $$\hat{H}=\int\text{d}\vec{r}\left(\hat{a}^{\dagger}\frac{\nabla^{2}}{2m}\hat{...
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What influence does a magnetic field have on a Bose-Einstein condensate? [closed]

Perhaps the answer could include the following possible scenarios: a static external magnetic field supports the formation of a BEC, the magnetic field maintains the BEC longer as the temperature ...
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What is a phonon and electron line width in phonon-electron interaction?

In case of phonon-electron interaction, I came across a term called "phonon linewidth", and I do not understand from where does it arises and what significance does it have. and why is it ...
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Difference between BEC and Superfluidity. Why is considered superfluid helium not a BEC?

I have not a clear idea what the difference between a BEC of weakly interacting bosons and superfluid is. My second question that could help me understand this difference is: why do alkali atoms form ...
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Boson Einstein condensation of free particles

Under Schrödinger's representation, for free particles without spin, each eigenstate vector is $\delta(x-x_0)$, corresponding to the eigenvalue $x_0$, each position in the 3-dimensional configuration ...
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Does superfluid have substructure? I mean does the substructure matter?

My main research interest is the gravitational wave. Recently, I and my academic brother watched a famous video about the superfluid. I read a review then came up with some questions. Here is the ...
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Quantum vs Classical Vorticities

Excepting the circulation quantization, what are the differences between classical vorticities (created in classical fluids) and quantum vorticities (BEC superfluids)?
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Soliton solutions of the Gross-Pitaevskii equation

The Gross-Pitaevskii equation admits soliton solutions such as: $$\psi(x)=\psi_0 sech(x/\xi),$$ where $\xi$ is the healing length defined by: $\xi=\frac{\hbar}{\sqrt{m \mu}}$, with $\mu$ being the ...
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How does particle-particle interactions affect superfluids?

Ive read that London approach of superfluidity was wrong because he took them as non-interacting bose gas molecules and got incorrect temperature dependence for density, but also one can take ...
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Hypersonic Bose–Einstein condensate

In this nature paper, a BEC is accelerated around a smooth ring-shaped waveguide within a vacuum chamber at UHV. The BEC reaches speeds up to 16 times the condensate's speed of sound. What is the ...
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What symmetry breaks in exciton condensation?

Recently the possibility of exciton condensates have shown up in some lattice TQFT models we've been studying, and I've been trying to learn more about them. Suppose that we have a band insulator with ...
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Homotopy group for spin-1 BEC

Homotopy group can be used to classify topological defects. The procedure is Find the Lie group $G$ that leaves the free-energy functional invariant when transforming $\psi$, where $\psi$ is the ...
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Can we use photons in a Bose-Einstein condensate? If not then why? If yes then how?

Can we use photons in a Bose-Einstein condensate? If not then why? If yes then how? Which kind of boson are we using in Bose-Einstein condensation?
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Confusion in understanding BCS ground state

Is there any absolute value BCS ground State? What confuses me is that the number of particles is not fixed, so when we add a BCS pair to the ground state, it will further decrease the ground state ...
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