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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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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Experimental challenges of increasing the size of a Bose-Einstein condensate

My question is partially inspired by this question. I know that BECs have been created whose side lengths are on the order of microns, while others have managed to make a side length of approximately $...
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Chemical potential in Bose-Einstein condensation

For a Bose gas, we know that when temperature goes to zero, chemical potential also reach to zero. At $T=0$ all bosons fall into ground state and thus chemical potential is also zero at $T=0$. Also ...
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Bose Einstein Condensation in Grand canonical ensemble

Why we develop formalism of Bose Einstein Condensation in framework of grand canonical ensemble ?
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Composite behavior of composite bosons with the help of entanglement

Are there any good books related to composite bosons using quantum information approach or that can help to understand Bose Einstein condensation of composite bosons?
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Bose gas Hamiltonian in second quantization with indefinite parity potential

In the book Bose-Einstein Condensation by Pitaevski, Lev; Petrovitch, and Sandro Stringari (Oxford University Press), the Hamiltonian for weakly interacting Bose gas reads as, $$H=\sum\dfrac{p^2}{2m}\...
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How self consistency condition works for a superconductors which is finite and does not have periodic boundary condutions?

So if a superconducting system has periodic boundary conditions the s wave superconducting order parameter calculation by self consistency condition is pretty straightforward. However what if I have ...
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Bose-Einstein condensation summation to integral

I have a question about Bose-Einstein condensation. Namely, people say that if we go from the summation over the number of particles to an integral using the density of states, we make a flaw in the ...
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How is it possible to produce a Bose-Einstein condensate of astrophysical dimension?

There is simple mechanism behind such a production and it suggests that a cloud made of bosons could collapse gravitationally into an equilibrium polytrope in the condensate phase. Assuming that ...
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Bose-Einstein condensation in 1D harmonic oscillator and its density of states

I have troubles understanding how (and whether) Bose-Einstein condensation works in 1-D harmonic oscillator. From my calculation it seems that in limit of infinite number of particles, almost all of ...
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Does zero resistance mean that there are no energy exchanging processes between particles in superconductor? [closed]

I was just knowing little bit about bose einstein condensate then I came across superconductor. In the bose einstein condensate particles have same energy levels and they can not escape the level or ...
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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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Is BEC the same as entanglement?

I understand that Bose Einstein condensate is: A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero. Under such ...
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Is the Bose-Einstein condensation a single particle phenomenon?

BEC occurs for noninteracting Bosons. Can we conclude that it can be described with a single particle? What is the significance of the number of the particles?
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Is there an intuitive reason as to why there is no phase transition to get to a degenerate Fermi gas?

Cooling a bosonic gas leads to a phase transition into the Bose-Einstein condesate. This is characterised by a symmetry broken ( U(1), by choosing a specific phase for the macroscopic wavefunction) ...
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What is the probability that a single-particle bosonic quantum state is occupied?

Unlike the Fermi-Dirac distribution function, the Bose-Einstein distribution function $$f(E)=\bar n_r=\frac{1}{e^{\beta(E-\mu)}-1}$$ can be greater than 1, and therefore, doesn't represent a ...
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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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Is BE condensation possible for photons, phonons and magnons all with $\mu=0$ (non-conserved particle number)?

Photons have zero chemical potential and their number is not conserved. The property of zero chemical potential is also true for emergent gapless excitations such as phonons in crystals and magnons in ...
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What is “quantum gas”?

I could not find a satisfying definition of this term from anywhere. Also, Can you please give some introductory level references to understand quantum gas?
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How to calculate density of states for different gas models?

There are a couple examples I'm trying to understand, all in a box/square of length $L$: For an ideal gas in 2-D with $\varepsilon=\frac{\hbar^2k^2}{2m}$:$$ D(\varepsilon)=\frac{L^2m}{2\pi\hbar}\,.$$ ...
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Link between integrability and soliton solutions

I have been doing some research on the properties and dynamics of solitons (in particular, solitons in superfluids) and several works and papers mention the link between solitonic solutions and ...
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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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Bose-Einstein Condensation in lower dimensions

Bose-Einstein condensation occurs at 3 dimensions. However, it is not possible to happen at 1 or 2 dimensions; in fact I am able to prove this myself. What is the explanation for this?
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Sudden release of condensate from trap - Ermakov equation - Scaling solution

This is related to the scaling solution of the hydrodynamic equations. I get a relation for the scaling parameter $b$: $\ddot{b} = -\omega^2(t)*b + \omega_0^2/b^3$ When the trap for the condensate ...
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What is the immiscibility condition in a Bose-Fermi mixture?

Also how can you approach that condition from a mean field approach? My intuition is you have to derive the free energy from the mean field energy and then do something with it, however, I'm not ...
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Bogoliubov approximation, coherent states and particle number conservation

I am slightly confused about an aspect of the Bogoloibov approximation for BEC. In it we take: $$a^\dagger (\vec 0)\approx \sqrt{N_0}$$ $$a(\vec 0)\approx \sqrt{N_0}$$ and find our Hamiltonian in ...
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Why is a collection of non-interacting bosons pathological?

In this lecture titled "Disorder and Interactions: From Spin Chains to Cold Atoms" the speaker Thierry Giamarchi claims that a collection of non-interacting bosons is totally pathological. His argues ...
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Understanding the behaviour of an interacting Bose gas

From the Bose-Einstein distribution it follows that a non-interacting Bose gas condenses into the Bose-Einstein condensate below a certain critical temperature. What happens when interactions are ...
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The invariance of BEC and curved space

I went to a lecture where the speaker explained that people could study space and cosmology and curved space by using BEC states. She tole me that the sound wave (mechanic wave) in BEC was equivalent ...
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Light at absolute zero? [duplicate]

What would happen to light at absolute zero? Any change of a property? Or to say it in different words, what would happen to photons at absolute zero? I have read that to slow down light, nearly to ...
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Cold atoms: how does evaporative cooling work?

I understand the principle of evaporative cooling (for the creation of a Bose-Einstein Condensate), but I do not find any reference which explains mathematically this process and which explains what ...
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Potential lineshapes of a BEC in a magnetic trap

We considere a Bose-Einstein Condensate (BEC) of atoms occupying a magneticaly trapped atomic state $|m_{F}=-1\rangle$. One can then use a radio-frequency field to extract atoms from the BEC by ...
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Why is matter wave field usually assumed to be be intrinsically stable?

In the paper "Collapse and revival of the matter wave field of a Bose-Einstein condensate" by M. Greiner, O. Mandel, T. Haensch and I. Bloch, it was stated that Bose-Einstein condensate (BEC) ...
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BEC and quantum liquid droplets

My first question is: Is atomic Bose-Einstein condensate a gas? My second question is: What are the difference between BEC and quantum liquid droplets?
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Berry curvature in rotating traps

A quantum system in a rotating (harmonic) trap is equivalent to a stationary system in the presence of a vector potential $\mathbf{A}$. The proof can be found in chapter 5 here, but in short it goes ...
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Feshbach -Resonance why are hyperfine structures important?

The hyperfine structure of energy levels around the ground state seem to enable Feshbach and be intrinsic to it. Why do we need hyperfine levels? I.e. why is Feshbach specific to ultracold atoms in ...
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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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Fermi-Dirac & Bose-Einstein: ideal gas, or more general?

The Fermi-Dirac and Bose-Einstein distributions are only for ideal gases or are applicable to more general systems? By ideal gases I mean all kind of systems composed by particles that do not interact ...
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Definition of Superfluid with no Bose-Einstein condensation?

A BEC with no superfluidity is referred to as Bose Glass (due to S. Yukalov to my knowledge). Is anyone aware of a similar definition for systems which exhibit superfluid behaviour but are not Bose-...
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Original 1925 paper by Einstein on Bose-Einstein Condensation?

Does anyone know if it is possible to retrieve the original 1925 paper by Einstein on Bose-Einstein Condensation? Possibly a translation into english, but german would be fine if no translation is ...
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Bogolyubov excitations in BEC

The dynamics of a Bose-Einstein condensate is usually described by the time-dependent Gross-Pitaevskii equation (TDGPE) $$ i\hbar\frac{\partial\psi(x,t)}{\partial t} = -\frac{\hbar^2\nabla^2}{2m}\psi(...
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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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Would dark matter (as a BEC) be captured by Black Holes, Neutron Stars, etc?

Suppose that dark matter is in the form of a Bose-Einstein Condensate, with a DeBroglie wavelength of ~10,000 LY. (There are some axion models of DM where the axions are in a BEC.) In this model, the ...
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Entropy of a Bose-Einstein condensate

I would like to understand why Bose-Einstein condensation can occur only for $d>2$ dimensions. Therefore, I want to know what the entropy of a Bose-Einstein condensate is. The grand canonical ...
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What would happen if very light particles (of large de Broglie wavelength) encountered a neutron star?

I want to consider the possibility of a very light particle being captured by a neutron star. (For the purpose of discussion, let us allow the neutron star mass (or radius) a tunable parameter, so ...
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Mean-field in Bose-Einstein condensate

Why we use a mean-field theory in Bose-Eisntein condensate? Is there another formulation that does not use a mean-field theory?
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Is every spontaneous symmetry breaking connected with a second order phase transition?

My question is rather clear: Is every spontaneous symmetry breaking connected with a second order phase transition? In many books (A.Zee QFT in a nutshell or also in P&S etc.) when they start ...
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Why there is no Knight shift for a spin-triplet p-wave superconductor?

In the Nature article: Spin-triplet superconductivity in $Sr_2RuO_4$ identified by ${^{17}}$O Knight shift https://www.nature.com/articles/25315 Authors state: For a spin-triplet p-wave ...
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Time Evolving Matrix Equation to find Eigenvalues

So I am looking at this paper (Instability and control of a periodically-driven Bose-Einstein condensate) and I am interested in solving equation 8, which reads $$i\frac{d}{dt}\begin{bmatrix} u(t)\\v(...
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Is gapless spectrum necessary for superfluity

In 3D interacting Boson system, the condensate leads to a gapless spectrum and superfluidity. The same gapless spectrum for 2D with quasi-condensate (correct me if it is wrong ). I am wondering if it ...