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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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Inflation of the Universe as Bose Einstein Condensate (Literature)

I'm searching for literature in the field of cosmological models which use a Bose-Einstein-Condensate (BEC) to model the process of inflation. Especially the analytical results the cubic BEC models ...
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Feshbach resonance - Magnetic Field/Spin Orientation

I have been reading about Feshbach resonance in ultra cold atoms and there were some areas I'd like to understand better/have questions about: i) As the atoms approach each other, can their spins be ...
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Clausius-Clapeyron equation and coexistence curve for Bose-Einstein Condensate

I am tasked with "deriving" the Clausius-Clapeyron Equation for the ideal Bose-Einstein condensate and plotting the coexistence curve. Yet, I am unsure how would I accomplish this task. Can I just use ...
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What is the wavefunction of a Bose-Einstein condensate made of composite particles?

The textbook answer is that a problem involving bosons is described by a wavefunction $\Psi(R_1,...,R_n)$ which is completely symmetric, and if non-interacting particles Bose condense, the ...
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about BCS-BEC crossover

In BCS-BEC crossover, we will get two self-consistent equations about the gap $\Delta$ and the chemical potential $\mu$. But when I compute the particle density: $n=\beta^{-1}\sum_k tr(G\frac{\partial ...
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How can Bose-Einstein Condensate improve our understanding of Dark Matter and Dark Energy?

There was this news a few days ago about NASA attempting to create the Coldest Spot in the Universe1 aboard ISS, to study further the properties of Bose-Einstein Condensate. I can understand that at ...
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Inflation and the build up of an inflaton condensate

Recently I've been reading up a bit on inflation and the subsequent reheating of the early universe. What has left me a bit confused, however, is that in all of the notes/papers that I've read so far ...
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Exact global phase of the Gross-Pitaevskii wavefunction

I will follow closely the book by Kaspar Sakmann chapter 3.2 about derivation of the time-dependent Gross-Pitaevskii equation. Starting from the time-dependent variational principle we arrive at the ...
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Bose-Einstein condensate effect

Does every boson gas go through the condensate effect? Could there be a boson gas with high energy (photons for example) that would have enough energy to be at different quantum states even at 0 K?
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Bose-Einstein Condensation at higher critical temperature

The critical temperature $T_{c}$ of a Bose-Einstein Condensate is directly proportional to $n^\frac{2}{3}$, where $n$ is the density of the system which is to be condensed. The current $T_{c}$ for ...
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Long distance limit BdG-equations

Consider the dimensionless Bogoliubov-de Gennes equations for the excitations in a BEC: $$ \begin{cases} \big(-\frac{1}{2}\nabla^2+2gn({\bf r}) - \mu -\omega\big) u({\bf r})-n({\bf r})g v({\bf r}) = 0\...
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Is nanoparticle a Bose einstein Condensate

I was reading about nanopartilces(NPs) and their properties. At several places I have read that NPs act as coherent body. I wonder if the Nps can be treated as Bose Einstein condensate (BEC) as ...
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MFT Approximation for Dilute Bose Gas

The Dilute Bose Gas has quartic Hamiltonian $$H=\sum_{k}\epsilon_k b_k^\dagger b_k+u\sum_{k\,k'q}b_{k+q}^\dagger b_{k'-q}^\dagger b_kb_{k'}.$$ It is said in a reference that Since the lowest ...
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376 views

Thermal wavelength and critical temperature for Bose-Einstein condensate

I'm stuck with derivation of critical temperature and thermal wavelength for Bose-Einstein condensate - all sources describe equations very briefly. Suppose we have a system described by Bose-Einstein ...
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Alternative derivation of Gross-Pitaevskii equation

I wanted to derive time-dependent Gross-Pitaevskii equation in an alternative way, but I don't know if something presented below is allowed. Hamiltonian is the following (I do not assume translational ...
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249 views

At the lambda point, why does specific heat capacity tend to infinity?

The specific heat capacity is the energy required to raise the temperature of unity mass by 1K, if at the lambda point all the bosons occupy the lowest quantum state, shouldn’t the specific heat ...
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Is a 2-atom BEC possible?

In theory, is it possible to generate a BEC with only 2 atoms? If not, what would be the lower threshold? I have a basic understanding of BECs: you consider only 2-atom interactions, pseudopotential (...
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Role of BEC in atom interferometry

What is the major advantage of using Bose-Einstein condensate in atom interferometry compared with other sources of atoms? Detectors measure population difference in two arms of the interferometer. I ...
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202 views

Bose-Einstein condensation as a phase transition

1.How does a non-interacting system exhibit phase transition? 2.Is partition function of BEC is non-analytic (just like in the ordinary phase transitions)? 3.What is the order of BEC phase ...
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Nonlocal interaction effects on bose-einstein condensates

I'm studying an interacting bose-einstein condensate using the energy functional proposed in this paper K. Huang, C.N. Yang, Phys. Rev. 105 $$ E\left[\phi\right] = \int d^3\vec{r} \left\{-\frac{\...
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136 views

Bose-Einstein Condensate

In lieu of recent research showing the possibility of obtaining the Bose-Einstein condensate Nq, in certain polymers is there any statistical mechanical way of figuring out the frequency with which ...
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126 views

How many ways are there to distribute M excitations of N identical particles among K=3 quantum harmonic oscillators?

I'm trying to numerically calculate a partition function of N non-interacting but identical particles in a 3D SHO. To do this, I'd like to know the degeneracy of $M$ excitations, $N$ indistinguishable ...
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221 views

Fock picture of bosonification in condensates

I want to understand how bosonification in a condensate must be interpreted in the Fock states picture Say i have uncoupled fermions in a set of states $E_1$, $E_2$ ... over the vacuum $E_0$. They ...
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675 views

What the difference between Bose-Einstein condensate and quantum spin liquid?

When matter gets close to absolute zero temperature, how does it becomes either BEC or QSL? I know in BEC atoms lose their individual id and becomes super-atom and as for spin liquid the alignment of ...
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Which is the difference between Josephson and Rabi oscillations?

Consider a bosonic Josephson junction, such as a Bose-Einstein condensate trapped in a double-well potential. What are Josephson oscillations and what are Rabi oscillations? In what do they differ?
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Hartree-Fock factorization

I am studying c-field methods applied to Bose-Einstein condensates to understand how one gets to e.g. the dissipative GPE. To do so, one splits the field operator for the Bose gas into a low- and a ...
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Free parameter in Bose Einstein Condensate

In Kapusta and Gale's Finite-Temperature Field Theory book, BEC is derived for a complex scalar by Fourier expanding $$\phi _1 = \sqrt2 \zeta \cos \theta + \sqrt{\frac{\beta}{V}}\sum_{n,\bar p}e^{i(\...
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Is it possible to use Bose-Einstein condensate for propulsion with today's tech?

Can one use the Bose Einstein condensate which we can produce today for space propulsion, as many theoretical concepts need negative mass and that is a property of Bose Einstein condensate, how ...
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What happens to the scattering cross section of two fermions with different spins at low temperature?

The scattering cross section for two identical fermions at low temperature is given by: $\sim 8\pi a_1^2(ka_1)^4$. I was wondering what happens if the two fermions have different spins - does it ...
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Chemical potential of a BEC

I know that the chemical potential of a BEC can be calculated with $\mu=\frac{\partial E}{\partial N}$, where $E$ is the energy and $N$ is the number of particles. For the Gross-Pitaevskii equation ...
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How to calculate a one-body reduced density matrix

I calculated eigenvalues and eigenvectors of a many-body problem for a SBEC (spinorial Bose-Einstein Condensate) in the SMA approximation . Then I can calculate the density matrix of this problem. ...
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Bose Einstein Condensation

We all know that the Bose Einstein distribution formula is $n=g_i/(e^{α+βi}-1).$ Where alpha is the derivative of constant number of particles that is supposed to be zero. But while studding Bose ...
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Mean energy of bosons gas

I am currently doing a question with regards to bosons gases and come across a sticking point. The question is as follows. For a gas of bosons at temperature $T$ below the Bose-Einstein ...
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JILA Rubidium-87 Bose Einstein condensate

Why was the observation of Bose-Einstein condensation by JILA considered so special? I was under the impression that they were not nearly the first group to observe it, since it was observed with ...
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Physical interpretation of Bogolyubov sound with zero momentum in BEC

The point with zero momentum in the spectrum of acoustic phonon corresponds to a translation of the crystal. Is there an interpretation like this of the Bogolyubov sound in BEC? I have read that in ...
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Why we can't write low energy effective field theory for a gapless system?

Assume that we have an Hamiltonian $$H=H_0+H_{int}$$ where $H_0$ has gappless excitations and $H_{int}$ has usual two body interactions. If $H_0$ were gapped I would able to get low energy effective ...
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Heating A Condensate

There is so much literature out there on Bose Condensates, that it is literally all about the cooling of a gas. But I am interested in the physics of the condensate heating up - can someone explain ...
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Where is the gauge symmetry in an ideal Bose gas?

It seems in the literature that there is a certain notion of a “macroscopic wavefunction” associated with a Bose-Einstein system (see this PSE answer) which exhibits a global $U(1)$-phase symmetry. ...
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How to write a wave-fuction of bose einstein condesate bosons in second quantization representation?

Can we write wave function of bose einstein condensation like this $|\psi \rangle=\frac{{c^{\dagger}}^N}{ \sqrt{N!}} |0\rangle$. Or it will be different?
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super bunching effect of bosons

Let say we consider a $N$ pair of elementry bosons (i.e $N$ composite bosons). At very low temperature these bosons will condense into the ground state. If we find the mean occupation number $\langle ...
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Order parameter and Bose-Einstein condensation

I want to study about order parameter and symmetry breaking related to bose einstein condensation in interacted system. Which book i should read? also i want to learn this in second quantization ...
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Free energy of non-interacting bosons in mean field

The result As a mathematician I am currently struggling to understand Tóth's Phase transition in an interacting Bose system. An application of the theory of Ventsel' and Freidlin. The free energy (...
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What is the super-bunching effects of composite boson?

What is the super-bunching effects of composite boson ?
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1answer
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Feshbach resonance and the Gross-Pitaevskii equation

I have a question about Feshbach resonance and the (generalized) Gross-Pitaevskii equation. If we consider a BEC at a finite temperature $T_{BEC}$ and a static mean-field thermal cloud at temperature $...
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Is mean and average occupation number same?

In Bose distribution we have formula to find number of particles in quantum state .Is mean occupation number and average occupation number same ?
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Can we have Bose condensation for bosons satisfying a dispersion relation $E=Cp^s$ $\forall$ s?

Suppose a dispersion relation $E=Cp^s$ where $C$ is a constant is known for a collection of massive non-interacting bosons. What is the way to find out whether there will be Bose-Einstein condensation ...
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First excited state during Bose-Einstein condensate

We know that the ground state is macroscopically occupied. What about the first excited state?
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Superconductivity and superfluidity in bosonic and fermionic condensates

Can bosonic and fermionic condensates explain superfluid and superconducting properties? Are they better than the theory of BCS and Landau? Edited: My question is based in this lecture pesentation ...
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Are condensates of gravitational waves possible?

Bose-Einstein condensation has been observed in a multitude of physical systems (cold atoms, exciton-polaritons, magnons to name a few). Notably in 2010 a BEC of photons was experimentally detected. ...
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Why the total nuclear spin is only 0 or 2 for singlet s-wave scatting with $M_F=0$?

when I read the lecture of Feshbach resonance, the lecture on page 15 said that it want to find all s-wave molecules for $M_F=0$. It said when the two atoms are singlet, the total nuclear spin is only ...