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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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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 ...
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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 ...
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Bose Condensation; interacting vs. non-interacting

I have some problems unifying, the two way I learned how a Bose condensate appears. The main problem is that the observables seem to be quite different. In statistical physics lecture one starts with ...
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BEC in a rotating disc

Goodmorning everybody, I have to run a numerical simulation of a Bose-Einstein condensate on a rotating disc. Now, my problem is that I became suspicious about the equation I'm using, since the final ...
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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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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 is the relation between Bose Einstein Condensate of Higgs and the Higgs field?

I have been wondering the relation between Higgs BEC and Higgs field. During reheating of the universe, people always claim the energy density of inflaton drops down like massive particles without ...
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Would cooling matter and antimatter to as close to Absolute Zero as possible allow them to coexist?

I was reading about Bose-Einstein condensates and how they affect matter and energy, and I wondered if "draining" that amount of energy from an atom of hydrogen and positronium would potentially allow ...
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Is there a classification scheme for linear classical field theories?

Central to a mathematical understanding of the Bogolyubov transformation is the study and classification of linear lattice field theories. What follows might be familiar to many people, but I just ...
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The Heisenberg Uncertainty in Bose Einstein condensates

What happens to the Heisenberg uncertainty principle, when a system reaches the Bose-Einstein condensed state? In our statistical mechanics lecture, we derived the following formula for the fraction ...
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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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Toward the establishment of non-equilibrium (quasi-equilibrium) magnon BEC theory

In 2006, Demokritov et al have reported that they have achieved the observation of quasi-equilibrium magnon Bose-Einstein condensation (BEC) in YIG at finite (room) temperature by using the method ...
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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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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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What's the role of BEC in superfluidity?

I'm writing about superfluid $^4$He. I've seen in some places that the transition to superfluid is attributed to Bose-Einstein condensation, but then in others that this model needs a massive amount ...
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Symmetry breaking and Ginzburg-Landau theory in Charge Density Waves (CDW)

I have been thinking about this problem, but cannot get a satisfactory answer. In CDW phase, if there is Periodic Lattice Distortion (PLD, or Peierls instability), one may think of the order ...
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What are fragmented condensates?

It is defined that if more than one eigenvalue of the one-body density matrix are macroscopically occupied the condensate is said to be fragmented. $$ n^{(1)},n^{(2)},...=\mathcal{O}(\mathcal{N}) $$ ...
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Can we 'dope' a fluid to make it become a superfluid?

The only element that can become a superfluid is Helium (He-3 and He-4) since it does not solidify not matter how cold it gets, hence it can reach the superfluid transition temperature whilst still a ...
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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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Matter-wave interference from free falling cold atoms

and another exam question, this is about current research: Interference of matter waves has been studied using ultra-cold atoms. The phase of a matter wave for free-falling cold-atoms at time $t$ ...
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How do I derive the critical temperature for bose condensation in two dimensions?

In class we derived the 3D case, but there's a step I don't understand: $$ N = g \cdot {V \over (2 \pi \hbar)^3} \cdot \int\limits_{0}^{\infty}{1 \over{e^{\left( E_p \over{K_B T}\right)}-1}} d^3 p = ...
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Calculate the matrix size for ground states BEC using difference with Gross–Pitaevskii equation

The Ground states BEC at $0$ temperature can be described by Gross–Pitaevskii equation as $(-\frac{\hbar^2}{2m}\nabla^2+V(r)+g|\psi|^2)\psi(r)=\mu\psi(r)$ We limit the BEC in 2D where $V(r)=\frac{1}{...
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Bose-Einstein Condensate bonding

How would a material bond with a BEC? Would it have valence electrons? If you were to have a couple hundred atoms in BEC, would they bond with a couple hundred other atoms, a lower amount that how ...
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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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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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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 ...
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What's the difference between laser light and incoherent classical light in terms of the path integral formalism?

So I believe I have the followings things straight: The electromagnetic field is described by the Lagrangian $\mathcal{L}=F_{\mu\nu}F^{\mu\nu}$. By writing down the Euler-Lagrange equations, or ...
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Differential equation with nonlinear nonlocal interaction

I am studying literature on the nonlinear Schroedinger equation. More generally, I am wondering how to tackle an equation of motion such as $\bigl(i\partial_t-\Delta\bigr)\psi(\vec{x},t)+V(\vec{x},t)=...
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What is a Yang-Gaudin Bose gas?

I'm a mathematicians with interests in physics and mathematical physics. I have some kind of understanding of Quantum Groups and I know that Gaudin Models are related to them in a way that I don't ...
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Can Bose-Einstein Condensates reflect gravitational waves?

This is a question based on the paper by Raymond Chiao in 2002 where it is stated: One of the conceptual tensions between quantum mechanics (QM) and general relativity (GR) arises from the clash ...
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How would a BEC respond to the gravitional force of a small mass so sensitively?

Recently I watched a BBC programme on anti-gravity, most of which was wishful thinking by NASA and BAe Systems 20 years ago. At the end of the program through, they did show what appeared to be a ...
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Numerical problem with Hartree-Fock equations for dilute Bose gas

I have to solve the following set of equations self-consistently: $$\begin{align} n_c(\mathbf{r}) & = \frac{1}{g}\left[\mu - V_{\rm ext}(\mathbf{r}) - 2 g n_{T}(\mathbf{r}) \right] \\[3mm] n_{T}(\...
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Gross-Pitaevskii equation and Bogoliubov approach

I have a dilute weakly-interacting bose gas and make the assumption that I have only s-wave scattering. Then I'm able to write the Hamiltonian as: $$ H=\sum\frac{p^2}{2m}a_p^{\dagger}a_p+\frac{1}{2V}...
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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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Bose-Einstein condensation in 3D

I have read in many books that BEC takes place in momentum space and in only 3-dimensions. What is meant by this statement?
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Deriving the “total” Bose Einstein density of states, including the condensate

Is is possible to derive the Bose-Einstein density of states containing the delta function representing the BE condensate?
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Different between droplet and a soliton

I am working on the droplet state in a Bose-Bose mixture. I have a question about the difference between the droplet liquid state and the soliton state: How we can treat a droplet state? And how do we ...
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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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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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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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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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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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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 ...