# Tagged Questions

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### Linear response theory for Gross Pitaevskii equation

I am trying to linearize the following GP eq: $$i\partial_{t}\psi(r,t)=\left[-\frac{\nabla^{2}}{2m}+g\left|\psi(r,t)\right|^{2}+V_{d}(r)\right]\psi(r,t)$$ The ansatz for ...
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### time-dependent Hartree-Fock for two-component bosons

How does the ansatz for the time-dependent Hartree-Fock wavefunction look like in the second quantization if we have two-component boson system and in one case the Hamiltonian commutes with number of ...
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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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### 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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### 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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### Linear Classical Field Theories: a Mathematical Classification

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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### 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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### 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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### Heisenberg uncertainty in Bose Einstein condensate

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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### Are gravastars observationally distinguishable from black holes?

Are observations of Hawking radiation at the acoustic event horizon in Bose-Einstein condensates consistent with gravastars? To reconcile the second law of thermodynamics with the existence of a ...
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### positronium BEC stability

After reading this article regarding Positronium BEC formation (for lasing purposes), there is a mention in there regarding Ps "up" atoms not annihilating with "down" atoms, the article is pretty ...
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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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### 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 ...
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### 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 ...
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### How many ways are there to distribute M excitations of N identical particles among K=3 quantum harmonic oscillators?

I'm trying to numerically calculate a partition function of N non-interacting but identical particles in a 3D SHO. To do this, I'd like to know the degeneracy of $M$ excitations, $N$ indistinguishable ...
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### Fock picture of bosonification in condensates

I want to understand how bosonification in a condensate must be interpreted in the Fock states picture Say i have uncoupled fermions in a set of states $E_1$, $E_2$ ... over the vacuum $E_0$. They ...
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### What the difference between Bose-Einstein condensate and quantum spin liquid?

When matter gets close to absolute zero temperature, how does it becomes either BEC or QSL? I know in BEC atoms lose their individual id and becomes super-atom and as for spin liquid the alignment of ...
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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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### Temperature dependence of phase transition in Quantum Hall Effect

Most phase transitions have a distinct critical temperature, depending on the parameters of the system. For example, the critical temperature of Bose-Einstein condensation depends on the particle ...
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### how to understand the effective Planck constant in BEC

In a BEC of N particles, people always say that the Planck constant for such system is effectively 1/N, instead of the original value of Planck constant itself. I suppose this argument is also proper ...
Parameters of the Bose-Hubbard model require the knowledge of the Wannier functions from the lowets band of the optical lattice potential $V(x) = V_{0}\sin^{2}(kx)$ according to equations: $$J = \int ... 0answers 12 views ### System of two perfect isolated bodies and infrared death What is the theory about a system of two bodies, which is perfect isolated from the environment? Take it as a Gedankenexperiment, where the two bodies are not perfect reflectors but the isolating ... 0answers 18 views ### Is absorption imaging in ultracold gases (BEC) a method destructive of the system? As of title, I wonder whether this imaging method heats the gas up to the loss of quantum coherence. Let's consider a specific example, a gas of 87Rb (Rubidium) and its D2 line. I might be wrong in ... 0answers 33 views ### Fugacity in Bose-Einstein condensate Just a simple question, I didn't manage to find out in my books... The fugacity z = e^{\beta \mu} in the case we have condensation in a bose statistics. Is it always 1 or z \to 1? In the ... 0answers 35 views ### Bose-Einstein condensate in external field at finite temperature Suppose at some finite temperature macroscopically large number of interacting bosons condense to form Bose-Einstein condensate (BEC) with some macroscopic wave function. There also exist excitations ... 0answers 18 views ### Interferometer based on atoms and gravitational field detection I know that ultra cold atoms can be used to measure a gravitational field, but how does this work exactly. More specifically, I know that an interferometer based on atoms can be used to make very ... 0answers 47 views ### Is a 2-atom BEC possible? In theory, is it possible to generate a BEC with only 2 atoms? If not, what would be the lower threshold? I have a basic understanding of BECs: you consider only 2-atom interactions, pseudopotential ... 0answers 24 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 - ... 0answers 17 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. ... 0answers 35 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} ...
From Carter's book Thermodynamics and Statistical Mechanics, the partition function of a bose-einstein gas in $d$ dimensions is  \ln(Z) = ...