Questions tagged [quantum-statistics]
234 questions
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Quantum statistics of branes
Quantum statistics of particles (bosons, fermions, anyons) arise due to the possible topologies of curves in $D$-dimensional spacetime winding around each other
What happens if we replace particles with branes? It seems like their quantum statistics…
Squark
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2 answers
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" or that "bosons want to stay as close as…
DoeJohn
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Anyons as particles?
I'm trying to understand the basics of anyons physics. I understand there is neither a Fock space they live in (because Fock is just the space of (anti-)symmetrized tensor product state, see e.g. Wikipedia), nor a (pseudo / fictitious) commutation…
FraSchelle
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What is parafermion in condensed matter physics?
Recently, parafermion becomes hot in condensed matter physics (1:Nature Communications, 4, 1348 (2013),[2]:Phys. Rev. X, 2, 041002 (2012), [3]:Phys. Rev. B, 86, 195126 (2012),[4]:Phys. Rev. B,87, 035132, (2013)).
But I have little knowledge about…
ZuoYou
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Why is (von Neumann) entropy maximized for an ensemble in thermal equilibrium?
Consider a quantum system in thermal equilibrium with a heat bath. In determining the density operator of the system, the usual procedure is to maximize the von Neumann entropy subject to the constraint that the ensemble average of the Hamiltonian…
joshphysics
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3 answers
Do distinguishable fermions obey the Pauli exclusion principle?
We know that fermions are identical particles and obey Pauli exclusion principle. But what is meant by distinguishable fermions? Does that mean, like proton and electron both are fermions but they are distinguishable because of charge? And if we put…
Tooba
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What causes Paulis Exclusion Principle?
Currently I'm taking an astrophysics class and has now come across electron degeneracy. As far as I understand, the reason why white dwarfs and such, does not collapse, is due to this, meaning that the electrons are so close together in the core,…
Denver Dang
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Is there a Majorana-like representation for singlet states?
I mean the Majorana representation of symmetric states, i.e., states of $n$ qubits invariant under a permutation of the qudits. See, for example, D. Markham, "Entanglement and symmetry in permutation symmetric states", arXiv:1001.0343v2.
By Majorana…
Joshua Herman
13
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2 answers
Irrelevance of parastatistics for space dimension > 2
Consider a system of $n$ undistinguishable particles moving in $d$-dimensional Euclidean space $E^d$. The configuration space is $M=((E^d)^n \setminus \Delta)/S_n$ where $\Delta$ is the diagonal (subspace where at least 2 particles have coincidental…
Squark
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2 answers
How is the degenerate electron gas state "degenerate"?
What is "degenerate" in the degenerate electron gas state?
Why is it called degenerate?
richard
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What is the relationship between Maxwell–Boltzmann statistics and the grand canonical ensemble?
In the grand canonical ensemble one derives the expectation value $\langle \hat n_r\rangle^{\pm}$ for fermions and bosons of sort $r$:
$$ \langle \hat n_r\rangle^{\pm} \ \propto \ \frac{1}{\mathrm{exp}[(\varepsilon_r-\mu)/k_B T] \mp 1} . $$
For…
Nikolaj-K
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Pressure of Bose-Einstein-Condensate in decreasing volume
Consider a Bose-Gas where $T_0$ is the critical temperature at which the temperature dependant chemical potential is $\mu(T_0) = 0$. Looking at the interval $ 0 \leq T < T_0 $ one can show that the pressure of the system is:
$$ P =…
Tera
- 512
10
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Non-Abelian anyons in the path integral formalism
Background
Homotopy classes in the path integral
Following the answer to this question about the role of homotopy classes in path integrals, it seems reasonable to me that, when calculating the propagator using the path integral formulation, we…
anon1802
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Examples of density operators $\rho=\sum\limits_n p_n|\phi_n\rangle\langle\phi_n|$ in which the states $\{|\phi_n\rangle\}$ are not orthogonal
The set of quantum states $\{|\phi_n\rangle\}$ in the definition of the density operator $$\rho=\sum\limits_n p_n|\phi_n\rangle\langle\phi_n|$$ need not be orthonormal, and need not form a basis. But unfortunately, in the examples that I have seen…
SRS
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Question about the existence of non-Abelian anyon
My question from reading this paper:
Michael G. G. Laidlaw and Cécile Morette DeWitt, Feynman Functional Integrals for Systems of Indistinguishable Particles. Phys. Rev. D 3, 1375 (971).
Definition: the configuration space of $n$ indistinguishable…
maplemaple
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