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Questions tagged [bosons]

Bosons are integer-spin particles that obey Bose-Einstein statistics.

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Probability of finding a particle in a two/three particle system

Let us consider a system of 2 identical particles, 1 and 2. Let, $ψa(1)$ is the amplitude of finding particle 1 at state $a$, and $ψa(2)$ is the amplitude of finding particle 2 at state $a$. Let N.F ...
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About the rigour of replacing spins by hardcore Bosons

In literature one sometimes find that spins are replaced by hardcore bosons. Formally one replaces spin operators $\sigma^- \leftrightarrow a$, $\sigma^+ \leftrightarrow a^\dagger$, $\sigma_z \...
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The importance of phase when defining fermions and bosons

In my lecture on indistinguishable particles, my lecturer is trying to illustrate to me the notion of particles being indistinguishable when considering that when we swap two particles in a box the ...
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Why do bosons tend to occupy the same state?

It is often said that, while many fermions cannot occupy the same state, bosons have the tendency to do that. Sometimes this is expressed figuratively by saying, for example, that "bosons are sociable"...
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Distribution of photons emitted by atoms

I am currently revising quantum gases, and a small but confusing thought experiment has been bugging me for a while. I understand the bookwork stuff on photons and how a photon gas in a blackbody ...
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Are composite bosons superradiant scattering candidates?

Massive bosons can experience superradiant scattering in an ergosphere. This can in principle be used as a power source. However, elementary massive bosons ($H^0,\,W^\pm,\,Z^0$) are short-lived. Are ...
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Bosonic commutation relations for force carriers?

Why are force carriers bosons? The easiest answer that I can give myself is that the gauge field $A_\mu$ is introduced like this: $$ \partial_\mu \rightarrow D_\mu = \partial_\mu+ieA_\mu, $$ so it ...
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3answers
118 views

Difference between $W^-$ and $\pi^-$

Maybe it's a very naif question, but what is the difference between a $W^-$ and a $\pi^-$? I mean they both change a $d$ into a $u$ right? $d \rightarrow u W^- \quad \text{and} \quad d \rightarrow ...
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A proof that Heisenberg's and Euler Lagrange's equations are equivalent in QFT [closed]

I asked this before (link, link) but I think people didn't understand what I was asking, so I am going to try again . Thanks for everyone that helped so far. In QFT, Heisenberg's equation is ...
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Can I distinguish a Bose-Einstein Condensate of composite bosons from one of elementary bosons?

The only requirement for an ensemble of particles to undergo a transition into a BEC is to be bosons. But two fermions also make a bosons. Are there physical, measureable implications of a BEC being ...
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Do anyonic statistics only arise from spatial degrees of freedom?

Elementary texts on quantum mechanics justify the existence of fermions and bosons using the simple argument that if we have a state of two indistinguishable particles $|a,b \rangle$, where $a$ and $b$...
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Do macroscopic bodies also show quantum nature at extremely low temperatures?

If we consider atoms or molecules and cool them to extremely low tempertures, will they also show quantum nature. Will their wave nature also get dominated? And if they are bosons, will they become a ...
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Example of phenomenon that occurs because Bosons don't obey exclusion principle

I am writing an essay targeted at undergrad level, non-science audience and I am trying to find another real world example of what is possible due to the fact that bosons are not subject to Pauli ...
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Will more than one composite boson can stay in the same energy state if constituent fermions has moderate entanglement?

Let say we consider two distinguishable fermions(bi-fermions) in compact form. The case when both fermions are existing as free fermions, they will obey Pauli exclusion principle. In other case if ...
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super bunching effect of bosons

Let say we consider a $N$ pair of elementry bosons (i.e $N$ composite bosons). At very low temperature these bosons will condense into the ground state. If we find the mean occupation number $\langle ...
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Why do composite bosons form a BEC?

I found this question here but it does not fully answer my question. The answer there was that "composite bosons can occupy the same state when the state is spatially delocalized on a scale larger ...
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42 views

What is the criteria of trapped ideal gas to form Bose-Einstein condensate (BEC)?

If we have ideal gas of bosons in a trapped harmonic potential, is the only necessary thing for BEC is a temperature less than the transition temperature? Or is there any other things we should keep ...
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What are soft theorems in context of scalr fields

What are soft theorems ? I tried reading Weinberg’s paper but couldn’t understand it, are there any resources on this ? I am very interested in the case of scalars.
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Wave function of a system of two identical fermions

In N. Zettili's 'Quantum Mechanics Concepts and Applications' [chapter 8, solved problem 8.3], we have to find wave function and ground state energy of a system having two identical fermions and in ...
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46 views

Can we consider oscillation of air column in the wind instruments as phonons subject to Bose- Einstein statistics ?

A flute is a wind instrument, which could be modelled as a resonance cylinder open at both ends. Any cylinder resonates at multiple frequencies. A skilful player produces a standing wave in the flute ...
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28 views

What is the super-bunching effects of composite boson?

What is the super-bunching effects of composite boson ?
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1answer
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Can we ever “measure” a quantum field at a given point?

In quantum field theory, all particles are "excitations" of their corresponding fields. Is it possible to somehow "measure" the "value" of such quantum fields at any point in the space (like what is ...
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Is possible to replace the photon as a force carrier of electromagnetic force with a sfermion-fermion relation pair model?

force carriers or messenger particles or intermediate particles are particles that give rise to forces between other particles. I read that A field’s spin is determined by how it transform if you ...
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Relation between entanglement and average number of modes that are taken by constituent particles of coboson

Let we have composite boson made of pair of fermions, and fermions are entangled with each other. The state of composite boson can be written as $ \sum_m \sqrt{\lambda_m} a^{\dagger}_m b^{\dagger}_m |...
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Indistinguishable particles and symmetrization of wavefunction

For 2 indistinguishable particles, we take the wave function to be $$\psi\pm (r_1,r_2) = A[\psi_a (r1)\psi_b (r2) \pm \psi_b (r1)\psi_a (r2) ]$$ where fermions get a - sign and bosons get a + But, if ...
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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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3answers
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Can we say that bosons attract each other?

We know that bosons donot follow Pauli exclusion principle, thus they can occupy the same state. But is it equivalent to say that bosons attract each other?
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1answer
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Quantum statistics from the (anti)commutation relations of the operators?

From a QFT point of view, the difference between bosons and fermions is that their creation/annihilation operators ($a^{\dagger}$, $a$ and $c^{\dagger}$, $c^{\dagger}$ respectively) obey the following ...
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1answer
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What happens if we consider at the level of calculation-definition (not physically) the photon have charge $\pm$ $1$ and the electron charge = $0$? [closed]

Warning: physically you do not have to change anything, photon still remain 'photon' and electron still remain 'electron'. I'm interested configuring an behavior in particle function exchange, not ...
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2answers
164 views

Is there such a thing as an anti-boson?

Can there be an anti-boson that when interacting with normal bosons, creates matter, like when anti-matter creates energy when interacting with matter? I know that anti-particles can be considered ...
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1answer
53 views

How to calculate the spin of an atom [duplicate]

If given an atom say ${^{108}_{47}Ag}$, what is the systematic way to determine its spin so that one knows whether it is a boson or a fermion?
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What are Cooper pairs in superconductivity? [duplicate]

At low temperature how does electron become Cooper pair and why can they pass through a superconductor without resistance? Please give quantum mechanical explaination.
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2answers
130 views

Why is boson spin number related to attraction and repulsion?

The accepted answer to this question says Since the electroweak interaction is mediated by spin 1 bosons, it is the case that "like (charge) repels like and opposites attract". Another answer ...
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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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1answer
41 views

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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1answer
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What happens during a weak interaction?

For e.g. during $\beta^-$ decay a $W^- $ boson is emitted changing an up quark to a down quark. This seems very weird to me as it looks like that up quark is not interacting with some other particle ...
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132 views

How do I know that gauge fields are bosons?

QED and the Dirac equation have field operators $\psi$ interact with a gauge field $A^{\mu}$. We identify $\psi$ as a fermionic field and $A^{\mu}$ as a gauge boson - the photon. Do we or can we ...
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Suppressed emission of composite particles

If a composite (pseudo)Goldstone boson $\phi$ emerges in a spontaneous symmetry breaking (similar to the mesons of QCD), is the emission of the $\phi$ particle suppressed in high-energy processes, i.e....
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Physics of a Second quantized Hamiltonian?

It is frequently seen that the (Bosonic) Hamiltonian $H=e a^{\dagger}a+f( a^{\dagger}a^{\dagger}+a a)$ is discussed and diagonalized using Bogoliubov transformation. My question is that what is ...
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1answer
76 views

Simulating the evolution of many-boson states

My task is to simulate the scheme presented in this paper: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.77.062316. In this question: Creating an operator for a polarizing beam splitter, I ...
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1answer
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Integrals involving Bose-functions (Computational)

In short, I'm looking for some advice/literature how to deal numerically with Bose function. My physical problem is to calculate a coupled set of Self-energies, thermal loop integrals, self ...
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103 views

Definition of Ohmic bath and damping force

I have read the Wikipedia article on quantum dissipation where it is talking about the bath spectral function. The bath spectral function provides a constraint in the choice of the coefficients $...
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1answer
113 views

How are computed Branching decay modes (for Higgs boson and from a general point of view)

I would like to know how are computed the branching decay diagram, like for example with Higgs boson represented below (source): It seems there are 5 ways of decays for Higgs boson. I suppose there ...
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2answers
95 views

Two bosons having the same state — how do you know there are two?

So, suppose that photons have the same quantum state. How do we know that there are 'two' photons having the same state, rather than just one? Is there a technical way to guarantee that there are ...
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115 views

Diagonalization of Quadratic Fermionic/Bosonic Hamiltonians

I'm currently reading Quantum Theory of Finite Systems by Blaziot and Ripka, and I have a question regarding the first few pages of chapter 3. In particular, the chapter takes on the task of ...
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1answer
29 views

Frequencies associated with boson/fermion operators

For a Hamiltonian like, $$\hat{H}=\sum_{k}\hbar\omega_{k}b_{k}^{\dagger}b_{k}$$ What does it mean to say that the frequencies $\omega_{k}$ must be positive if $b_{k}$, $b_{k}^{\dagger}$ are boson ...
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1answer
107 views

Fermionic and Bosonic physical Hilbert spaces - are they actually Hilbert spaces?

Consider two identical particles $A$ and $B$. The combined Hilbert space $\mathcal{H}_A\otimes \mathcal{H}_B \newcommand{\ket}[1]{\left|#1\right>} \newcommand{\bra}[1]{\left<#1\right|} $ is a ...
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88 views

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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1answer
116 views

Hard-core bosons and fermions - spinless?

The introduction to this paper about bosonic atoms expanding in an optical lattice says the following: Are hard-core bosons mapped to spinless fermions? Because this link shows the mapping ...
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What experiments can measure the eigenvalues of the particle exchange operator

In a system with two indistinguishable particles, the eigenvalue to the particle exchange operator $\hat{P_{ij}}$ is $+1$ if the two particles are exchange symmetric, ie. bosons, and $-1$ if they are ...