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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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What does sub-bosonic behavior of composite boson means? [on hold]

Let say we consider two distinguishable fermions(bi-fermions) in compact form. This pair of fermions make a composite boson. Now we develop formalism to check either our composite bosns is like a pure ...
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What happens when we cool down the gas of non-identical particles?

For gas of identical particles, when we cool it down to extremely low temperature we can see one of two types of behaviour depending on the symmetry of wavefunction with respect to argument ...
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What is effective mean value? [closed]

For counting the number of particles in any specific state we use effective mean value $\langle \hat{N} \rangle $ instead of number operator $\hat{N}$ in ensemble. I want to know what is the advantage ...
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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 are the anti-commutation relations needed to be fulfilled by fermionic Bogoliubov transformation?

Bogoliubov transformations are a well used tool to get rid off interaction terms in second quantized Hamiltonians. I'm interested in the fermionic Bogoliubov transformation used in BCS theory, e.g. \...
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Is the ground state a Schrödinger cat state?

Consider the following Bose-Hubbard Hamiltonian which describes a Bose-Einstein condensate confined in a two-well potential: $$ H= -T(a_L^\dagger a_R + a_L a_R^\dagger ) + \frac{U}{2}(n_L^2+n_R^2-...
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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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In what conditions we can take ground state energy $E_0$ equal to zero?

Like in 3D harmonic oscillator , $E_m = {h} \omega {(m_x +m_y + m_z + 3/2)}$, At ground state energy $m=0$ and $ E_m = h \omega(3/2)$. While discussing Bose-Einstein condensation, for calculations we ...
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Bose condensate in 4d

Could a boson gas condensate in a hypervolume $V$ in 4D? How can I find its critical temperature and the heat capacity? In the books it just said volume $V$, it does not specify the dimension. My ...
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Why we consider identical particles for Bose-Einstein condensation?

Why we consider identical particles like identical composite bosons for BEC. Why we do not consider non identical particles of differnt masses etc?
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Why do bosonic atoms behave like they do?

Why do bosonic particles behave the way they do? Why doesn't the Pauli exclusion principle affect the electrons, protons, and neutrons of the atoms at temperatures close to absolute zero? How does ...
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“General” for time evolution of quantum state

I am reading a book in which at some point they find the time-evolved wavefunction $\phi_0(\mathbf{r},t)$ from the static $\phi_0(\mathbf{r})$. They say that "employing the Heisenberg time evolution ...
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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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What is *diagonal* long range order?

I have seen this question about off-diagonal long range order in superfluids. What’s the difference and the significance between long range diagonal and off-diagonal long range order?
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Bose-Einstein distributions when combining different sources of photons

In a telescope, the photons coming from the object you want to observe will pass through a lens, which emits its own photons from heat. It's possible to calculate a B-E distribution from both these ...
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What is quantum fluctuation in the Bose-Einstein condensates theory?

I would like to understand what quantum fluctuation really means. I think it's the particles that are not in the ground state. Am I right? But then, what are the differences between quantum ...
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What is the link between superfluids and BEC?

i’m studying superfluids (in particular $^4 He$) and one of the first theorical apporoach was with Bose-Einstein condensation and i know that we can calculate the $T_c$ and it is close to the the ...
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why for two level system we consider both energy level while finding number of bosons in ground state?

Let suppose we have N number of particles in two level system. .Effective number of cobosons in ground state is $ <n_0>$ that can be written as $<\hat{n}_0>= Tr [\hat{n_0}\rho ]$ where $\...
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Partition function for an interacting bosonic mode

Let us assume a single bosonic mode, in equilibrium with a reservoir. For a non-interacting Bose gas, the partition function becomes $\mathcal{Z_\text{nonint}}=\sum_{N=0}^\infty e^{-\beta(\epsilon-\...
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Volume in first octant

Here we are finding number of state less than energy E for particle trapped in 3D harmonic potential .For large value of E as compare to hw , we assumed energy levels as continuous.And we introduces ...
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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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A deformed Creation and Annihilation Operetors

When we talk about para-bose oscillators under a chemical potential $\mu$ we might bring up the Eq. $$\frac{1}{e^{\beta(E-\mu)}-1}$$ Seems natural to think that now the vacuum energy of the ...
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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 ...