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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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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Bose-Einstein condensation and phase transition

I would like to ask the following question for which I cannot find a definite answer in the literature. Of what ORDER is the phase transition leading to Bose-Einstein condensation for a ideal and ...
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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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263 views

Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?
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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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431 views

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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269 views

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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109 views

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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165 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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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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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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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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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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441 views

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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512 views

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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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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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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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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1answer
412 views

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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1answer
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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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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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141 views

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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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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1answer
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Is Bose-Einstein condensate in the optical lattice a single mode condensate?

I recently read about BEC loaded into the optical lattice p.200 Looking at a condensate released from a lattice after a time of flight typically on the order of a few milliseconds amounts to ...
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1answer
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Does spin affect the expression for a Bose-Einstein Condensate's critical temperature?

In an assignment, we were asked to find the critical temperature of a collection of Rubidium-87 atoms. The answer used an expression derived for spin-zero bosons in Schroeder's Thermal Physics (which ...
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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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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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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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Phase change into Bose-Einstein Condensate

I am a high school chemistry/physics teacher and I was just wondering what the phase change into/out of a Bose-Einstein Condensate is called? Thanks!
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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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123 views

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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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 ...