Questions tagged [bosons]

Bosons are integer-spin particles that obey Bose-Einstein statistics. Two bosons can occupy the same quantum state.

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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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Bosonization and Commutation Relation

I'm playing a bit with bosonization $ψ→:e^{-φ}:$ and $ψ^*→:e^{φ}:$ in the sense that $$ \Bigg\langle 0_\mathrm{F} \Bigg|∏_{i=1}^nψ(z_i)ψ^*(w_i)\Bigg|0_\mathrm{F}\Bigg\rangle = \Bigg\langle 0_\mathrm{...
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Can fermions composing a boson ignore Pauli's principle?

After a discussion with a fellow student, we came above this problem asked as question in the title. A similar question was answered here. But it doesn't answer the question for us. In a BEC, many, ...
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277 views

Physical interpretation of the chemical potential in Bose and Fermionic gas

I understand that both Fermions and bosons have the chemical potential $\nu <0$ when it is T>0, but still behave classically, the fermions would increase its chemical potential at T=0, whereas the ...
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What does the symmetrization postulate mean for the decomposition of the $N$ particle Hilbert space $\mathcal{H}^N$?

Suppose you have $N$ particles, each of which can occupy any of $s$ states. In general, you can write the $N$ particle Hilbert space $\mathcal{H}^N$ as a product of $1$ particle Hilbert spaces $\...
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Fields: Bosons vs Fermions

Reading Student Friendly Quantum Field Theory by Robert Klauber and he made me realize I've taken as fact for some time that bosons are the "force carriers" in QFT, without really understanding fully ...
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295 views

Can the mass of longitudinal and transverse W bosons be measured separately?

Some higgsless unified models of particle physics predict that the mass of longitudinally polarized W bosons and the mass of transversely polarized W bosons are different. In those models, a ...
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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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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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144 views

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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223 views

Finding the state and wave-function for two identical spin-1 bosons trapped in one-dimensional harmonic oscillator

My question concerns the validity of my approach to a problem and wether the answer is correct. I am tasked with writing the state vector(s) and wave-function(s) for when two identical spin-1 bosons ...
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55 views

Do we expect to find a dark energy boson?

Is dark energy expected to be a force carrying particle that interacts with all forms of matter?
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135 views

Why do we need to suppose the chemical potential is zero in this situation?

I've been working on some statistical mechanics problems and one of them asks to compute the pressure with chemical potential zero of a boson gas whose particles do not interact and whose energies are ...
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515 views

Why is the isothermal compressibility of the ideal boson gas larger than of the classical ideal gas?

Recently I came across (or well, derived in a lecture) the isothermal compressibility for an ideal boson gas. This was done in the context of statistical physics, using the quantum version of the ...
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Free bosons with an attractive/repulsive defect

Consider a system of non-interacting bosons hopping in a qubic lattice in 2D or 3D. A single site of the lattice is an attractive/repulsive defect. Formally, let $H=-t\sum_{<i,j>}(a_i^\dagger ...
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Could a fundamental particles electric charge or spin be 'given' to them by bosons?

I understand the statement "The Higgs Boson gives particles their mass" is not entirely true, but at least captures the spirit of the idea. What I find curious about it is that mass is an almost ...
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254 views

photon and Z boson interference?

I'm not certain that this question will make sense, but here goes... In most monte carlo generators, when Z events are produced, there is a lower mass cutoff on the Z pole. I've been told that this ...
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1answer
139 views

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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30 views

Spin 0 boson interaction

I have a question regarding the interaction of two spin 0 bosons in a shared harmonic oscillator. What would their first excited state be? I'm thinking that the total state has to be symmetric so ...
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27 views

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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38 views

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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1answer
49 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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72 views

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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150 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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238 views

Can matter/antimatter “annihilation” produce “dark matter”?

I was thinking about the following reasoning: If a matter and antimatter reaction produces energy, this energy would have particles itself. I found out (reading...) that one (the main?) product are ...
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Mass softening for high-energy interactions?

It is well known (see, e.g., eq. (2) in this paper) that the coupling $g$ of composite, fermion-bilinear bosons (e.g. pomerons) to fermions (e.g. quarks) decreases above the compositeness scale $\mu$ ...
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310 views

Interpretation of antiferromagnetic magnons dispersion relation

The dispersion relation of magnons in a ferromagnetic 1d lattice is \begin{equation} \omega(k)=\omega_0\big[1-\cos(ka)\big] \end{equation} where $\omega_0$ is a constant and $a$ is the spacing ...
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69 views

commutation relations for many-body permanents

I'm interested in understanding the many-body generalization of the canonical commutation relations. I.e. commutators of the form $$ [a^\dagger_I, a_J] $$ where $I,J$ are multi-indices with the ...
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25 views

The ratio between $m_W$ and decay distance of hadrons resulting from pp collision

A pp collision results in: $pp\rightarrow t\overline{t}\\ t \rightarrow bW^{+}\\ \overline{t} \rightarrow \overline{b}W^{-}\\ W^{+}\rightarrow u\overline{d}\\ W^{-}\rightarrow\overline{u}d$ From b ...
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371 views

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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23 views

Is it possible to compute the kubo conductivity of bosons in disorder via mean-field theory?

The kubo conductivity is computed essentially from the current-current correlation function. This works fine when there is no or a periodic potential, as there are a number of ways that can be found ...
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475 views

Finding states of a system of 2 identical bosons (including spin)

I'm trying to find the ground state and first excited state for 2 identical bosons in an infinite square well. I know that both states are degenerate and the spatial and spin parts of the wave ...
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105 views

Product of expectation values for multimode operators

If $A_{n}, B_{n'}, C^{\dagger}_{n''}, D^{\dagger}_{n'''}$ are multimode field operators that obey the bosonic commutation relations, under which circumstances the product of expectation values $\...
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How to relate the number of bosons (fermions) with the number of vertices and external (internal) bosons (fermion) lines?

I am following the QCD book: "QCD: Renormalisation for the Practitioner" by P. Pascual, R. Tarrach. In chapter 3, page 64, equation III.13 they relate the following quantities: Let us consider a ...
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Capturing superfluid condensation with exact diagonalization

Doing exact diagonalization on bosonic systems is tricky, because the possibility of multiple occupancy means that even the single-site Hilbert space is infinite-dimensional. It's my understanding ...
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107 views

Can we measure the energy of one of several identical particles?

Suppose we have a many-particle system described via a many-particle wavefunction that involves single-particle states $\lvert\lambda_{a}\rangle$, $\lvert\lambda_{b}\rangle$, $\lvert\lambda_{c}\rangle$...
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Why is this equation regarding boson coherent states true?

I'm reading the proof of the closure for boson coherent states and it involves the following step: $$ \int \prod_{\beta}\frac{\mathrm d \phi^*_{\beta} \mathrm d \phi_{\beta}}{2 \pi i} e^{-\sum_\beta \...
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Quantum Mechanisms for Isotope Fractionation

Are there any quantum properties that would enable isotope fractionation? For example, atoms with odd versus even numbers of neutrons are fermions and bosons, respectively. Has any work been done ...
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145 views

How to understand the matrix behind a Hamiltonian?

thanks to the answers I received to my previous questions, I could derive correctly an elegant partition function for my problem which resembles a second quantized model taking the particles to be ...
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216 views

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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How to construct general multiparticle states that respect fermionic or bosonic symmetry?

Background: The arena is fixed particle number nonrelativistic quantum mechanics. The state space is $$ \mathbf{H}(1)=\mathcal H\otimes\mathcal S, $$ where $\mathcal H$ is an "orbital" state space ($L^...
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Grand Canonical derivation of Bose-Einstein and Maxwell-Boltzmann statistics

So, our professor introduced the Bose-Einstein statistics by deriving the Grand Canonical Partition function of a boson system associated to a single energy state $\epsilon_r$. So the formula is: $$\...
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Spacial Wavefunction Symmetries and Identical particles

I was reading this and it mentions in the 3-electron section, that for a spacial wave function to be symmetric under fermion swapping, it must be a function of even parity. Similarly for anti-symmetry ...
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Single atom states with energy 0, probability and occupation number fermions and bosons

Two mutually non-interacting atoms are trapped in a double-well potential in equilibrium at a temperature $T$, such that an atom can only occupy two possible single- atom quantum states, $Ψa(x)$ and $...
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144 views

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

Let us consider a system of 2 identical particles, 1 and 2. Let, $ψ_a(1)$ is the amplitude of finding particle 1 at state $a$, and $ψ_a(2)$ is the amplitude of finding particle 2 at state $a$. Let N.F ...
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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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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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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 ...