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1answer
67 views

Hamiltonian of weakly-interacting Bose gas

I try to derive the Hamiltonian for a weakly-interacting Bose gas. I am stucked right now at this step, could someone explain it? Thank you! Best Michael
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1answer
45 views

How to add Langevin terms to the semiclassical Bose-Hubbard model?

I would like to add Langevin terms to the Hamilton equations of motion of the semiclassical Bose-Hubbard model. Here's what I have: I start with the standard example of Brownian motion, a particle ...
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0answers
25 views

Software for BEC dynamics in optical lattice

I am looking for a quantum chemistry software that deals with Bose-Einstein condensate in optical lattices (1D, 2D, 3D). I am interested in full many-body Schrodinger equation (two-body interactions - ...
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0answers
18 views

calculation of first order coherence function

I have solved a gross-pitaevskii equation for bose-einstein condensate. The wavefunction which i have obtained has the property which its square shows the number density of atoms in the condensate. ...
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0answers
58 views

Could we Bose-condense Higgs bosons?

Apart from the obvious problem that we'd have to create enough of them and somehow not let them decay, is there anything that would prevent a Higgs boson condensate?
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0answers
106 views

To what extent is the Standard Model vacuum made of a Bose-Einstein condensate of Higgs bosons?

Note: I very well understand spontaneous symmetry breaking of global symmetries and the Higgs mechanism. I want to know to what extent the Standard Model vacuum is made of a Bose-Einstein condensate ...
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1answer
36 views

BEC in interacting systems

What is your thought on the following statement: "any system of (weak/ strong) interacting bosons, in liquid phase, will form a condensate at T=0". Any example or counter-example ? Will dimensionality ...
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0answers
61 views

Is there a local canonical ensemble partition function for a Bose-Einstein gas?

The grand canonical partition function for a Bose-Einstein gas is $$ Z_{\text{grand bos}} = \exp \left( \sum_{j=0}^{\infty} -\ln \left( 1-e^{\beta(\mu-\epsilon_j)} \right)g_j \right) $$ where $\beta$ ...
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1answer
47 views

Why classical open system and Bose-Einstein condensate are not fundamentally the same?

The classical partition function for an open system is given as $$ Z_{\text{max}} = \sum_{N=0}^{\infty} \dfrac{h^{-N}}{N! } \prod_{j=1}^{N} \left( \sum_{i=0}^{\infty} e^{-\beta (E_{ij}-\mu)} g_{i} \...
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0answers
36 views

What does the particle to volume density physically mean for Bose-Eisenstein condensate?

The average number of particles $\langle N\rangle$ for a Bose-Eisenstein condensate in 3D is given as $$ \dfrac{\langle N\rangle}{V} = \dfrac{V^{-1}}{e^{\beta (0-\mu)}-1} + \int_{0}^{\infty} \dfrac{V^{...
0
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1answer
91 views

Why do different phases of matter coexist?

Say at a critical temperature $T_c$ there is a phase transition. If we had water, $T_c$ for the liquid-solid transition is $0 ^\circ$C. If we left a block of ice at $1 ^\circ$C for a bit, it will ...
3
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1answer
173 views

What does chemical potential $\mu = 0$ mean?

First off, just to be clear, the chemical potential being equal to zero is different from not having a chemical potential at all (e.g. a photon gas)? Now: physically, what does having chemical ...
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0answers
45 views

bose einstein phase transition

From Carter's book Thermodynamics and Statistical Mechanics, the partition function of a bose-einstein gas in $d$ dimensions is $$ \ln(Z) = -\int_{0}^{\infty}\ln(1-e^{\beta(\mu-\epsilon)})c_d\epsilon^{...
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0answers
33 views

How is it possible to combine various techniques in cold atom experiments?

I’ve been reading about laser-trapped cold atoms (6Li in particular, which is a fermion) and was amazed at the number of things to keep track of in the experiments, just to gain that degree of control ...
4
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1answer
126 views

Interactions and scattering length in Feshbach resonances

In the context of cold atoms, one can make use of the Feshbach resonance mechanism to alter the sign and value of the two-particle scattering length by applying and varying an external magnetic field. ...
0
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1answer
75 views

physics of the beaker experiment for superfluid helium

here is an illustration and explanation of the beaker experiment over superfluid helium: So, according to this experiment, can anyone say what is the cause? I mean the superfluids are disconnected ...
0
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1answer
96 views

What happens at lambda point?

When Boson gas approach lambda point (no matter from superfluid side or liquid side),the heat capacity tend to diverge, doesn't this mean that we can never drive the gas through lambda point?(cause we ...
0
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1answer
26 views

Ground state energy of Bose Einstein gas

I am wondering why BE gas ground state contribute no energy.if so, then dose it mean that if we drive the Bose gas to absolute zero,then it doesn't own any energy?
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0answers
37 views

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 ...
0
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1answer
71 views

How do I evaluate the angular momentum of the wave function?

I'm working with Bose-Einstein condensates and running a 2D single component Gross-Pitaevskii equation solver for the simulations in MATLAB. The way it works is that it numerically solves the GP ...
4
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1answer
93 views

What happens to the planck distribution if the temperature is set to zero?

BE Problem I am currently working on modelling the density of states and optical conductivity of graphene utilizing the GW algorithm. In calculating the exchange self energy of the system, the ...
0
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1answer
35 views

Phase correlation between an excited and ground state in a BEC

What happens to the phase of the atom that gets kicked out of the atomic condensate? Is it completely random or does it have some correlation with the condensate phase?
-1
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1answer
122 views

Zero volume at zero Kelvin

Why does the volume of a gas become zero at 0 Kelvin? Can a Bose Einstein condensate be considered as matter? (I mean the volume becomes zero)
4
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1answer
273 views

Feshbach resonance in simple terms

I was reading up Feshbach resonances in cold atoms and I was unable to grasp the concept. I will tell you what I have understood. We consider two body scattering processes elastic as well as inelastic....
3
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1answer
510 views

BCS-BEC crossover

It would be really helpful if somebody could describe what does one mean by a BEC-BCS Crossover. I was going through articles available on the topic, but I was unable to grasp the gist of the topic.
0
votes
1answer
127 views

Application of BEC in Helium-4

By using the formula for Transition Temperature, we can obtain the Transition temperature for Bose Einstein Condensation to occur at 3.14 K, however, it shows the properties of superfluidity at 2.18 K....
3
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1answer
412 views

Why is Bose-Einstein condensation a phase transition?

Bosons may succumb to a Bose-Einstein condensation at a certain critical temperature $T_c$, thus entering the BEC phase. The only thing I know about the BEC is that since we are talking about bosons ...
3
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1answer
42 views

Why is the atom loss rate enhanced at the Feshbach resonance?

At the Feshbach resonance, the scattering length is enhanced. But why is the atom loss also enhanced?
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0answers
274 views

Linear response theory for Gross Pitaevskii equation

I am trying to linearize the following GP eq: \begin{equation} i\partial_{t}\psi(r,t)=\left[-\frac{\nabla^{2}}{2m}+g\left|\psi(r,t)\right|^{2}+V_{d}(r)\right]\psi(r,t) \end{equation} The ansatz for ...
0
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1answer
95 views

Bose Einstein Statistics and Bosons

For Bosons obeying Bose-Einstein Statistics, Why is energy taken to be zero at 0K, while for Fermions the energy is not zero at 0K.
1
vote
1answer
123 views

What has been observed as the “Hawking radiation” emitted by a black hole analog?

I've noticed this paper which explains that they have observed the "Hawking radiation" emitted by a black hole analog. In which sense the Bose-Einstein condensate described by the paper can be ...
0
votes
1answer
90 views

chemical potential in BEC decreases in temperature

For a bose gas we can calculate the average number of particles through $$N = \int_0^\infty \rho(\varepsilon)n(\varepsilon) d\varepsilon$$ where $\rho(\varepsilon)$ is the particle density for energy $...
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0answers
76 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 ...
1
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3answers
114 views

Why can't classical particles make Bose-Einstein condensate?

Where the quantum mechanics enters in BEC, why can't (non-interacting) classical particles condense?
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0answers
160 views

What is the largest number of bosons placed in a BEC?

What is the record for the largest number of bosons placed in a Bose-Einstein condensate? What are the prospects for how high this might get in the future? EDIT: These guys reported 20 million ...
1
vote
1answer
60 views

single-mode approximation in spinor F=1 BEC with dipolar interactions

How can a single-mode approximation be justified in spinor F=1 BEC with dipole-dipole interactions? Or maybe this kind of approximation will never take place and condensate components are always ...
2
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0answers
38 views

Why do electrons form Cooper pairs below certain temperature? [duplicate]

Just a heads up - please make this answer understandable to around 1st year degree level physics - not PhD research. So I can understand it - thanks. 1) In solid state physics, why is it that below a ...
1
vote
1answer
291 views

How to derive the critical temperature for Bose-Einstein condensation of photon?

I found in Nature magazine that photon can have Bose-Einstein condensation. But I have a question how to derive the critical temperature for photon? Because the chemical potential of photon is zero ...
3
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1answer
82 views

When would the Gross-Pitaevskii equation break down as $a\rightarrow \infty$?

It is now common to use Feshbach resonance to tune the s-wave scattering length of a Bose-Einstein condensate. Apparently as $a\rightarrow \infty$, the GPE would break down. The reason is that it ...
1
vote
1answer
83 views

How do you actually cool the atoms to create the Bose-Einstein Condensate?

What is the actual way you cool atoms to a low enough temperature that you can observe their quantum behavior at a macroscopic level, like in the Bose-Einstein Condensate? http://en.wikipedia.org/...
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0answers
47 views

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{\...
3
votes
1answer
145 views

Superfluid $\Leftrightarrow$ Bose-Einstein condensate?

On the Wikipedia page on superfluidity one can find the sentence not all Bose-Einstein condensates can be regarded as superfluids, and not all superfluids are Bose–Einstein condensates. So I was ...
4
votes
1answer
156 views

Bose Einstein condensation and macroscopic occupation

If have been thought, that Bose Einstein condensation occurs of the ground-state is occupied macroscopically, so $n_0\in \mathcal{O}(N)$ when performing the thermodynamic limit. So naively, this ...
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3answers
202 views

In a radioactive Bose-Einstein condensate, would all the atoms disintegrate simultaneously?

They're all supposed to do the same thing - so I suppose they would? Also, would the resulting half-life be the same as that of the individual atoms it is made up of?
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0answers
78 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 ...
1
vote
1answer
251 views

Ground state Phase Diagram of Bose-Hubbard Model

The Hamiltonian of Bose-Hubbard model reads as $$H=-J\sum\limits_{<i,j>}b_i^{\dagger}b_j+h.c.+\frac{U}{2}\sum\limits_{i}n_i(n_i-1)-\mu\sum\limits_in_i~~~~~~~~~(1)$$ For this we plot phase ...
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0answers
137 views

Temperature of Bose-Einstein-Condensate in space

Recently I heared a talk by Bill Phillips, who talked about the coldest temperatures in the universe. Among others, he sayed that the coldest temperatures created at the moment are BECs, which can ...
3
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1answer
237 views

Hamiltonian with Dirac Delta function

I've to compute this expression $$ \hat{H} ~=~\frac{1}{4}g_2\int d^3R\int d^3r\ \bar{\Psi}(\vec{R}+\frac{\vec{r}}{2})\bar{\Psi}(\vec{R}-\frac{\vec{r}}{2}) $$$$ \times \left[ \delta(\vec{r})\nabla_{\...
2
votes
1answer
292 views

Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation \begin{...