Tagged Questions
1
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0answers
51 views
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 ...
0
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0answers
39 views
Application of adiabatic quantum algorithm and quantum annealing algorithm [closed]
I am looking for a paper where the same problem is solved with both the adiabatic quantum algorithm and quantum annealing algorithm along with comparison between their performances. Any one with any ...
3
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1answer
140 views
Phase space in quantum mechanics and Heisenberg uncertainty principle
In my book about quantum mechanics they give a derivation that for one particle an area of $h$ in $2D$ phase space contains exactly one quantum mechanical state.
In my book about statistical physics ...
4
votes
2answers
88 views
Independent systems and Lagrangians
Definition 1:
The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
2
votes
1answer
110 views
Energy density of a quantum mechanical ensemble
How do we determine the energy density of a given system? I have seen that the density operator
$$\rho~=~\frac{\exp(-\beta \hat{H})}{\text{tr}(\exp(-\beta \hat{H}))}.$$
What does this mean exactly ...
1
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1answer
69 views
Maximizing Multiplicity of Einstein Solid == (Temperature = $\infty$)?
If I have a system consisting of 2 Einstein solids (A and B) is it equivalent to say that maximizing the multiplicity of the ...
3
votes
2answers
102 views
What is wrong with these ways of determining the mean occupation number?
Could anyone point out what went wrong in this argument?
Setup:
We have a system with 2 energy levels say with energies $0,e$ respectively.
We consider the grand canonical ensemble for the system ...
1
vote
0answers
26 views
Is there anything to prevent paired-up neutrons from a complete overlap
The reason "neutrons don't overlap", as DarenW explained it, has to do with intricate forces at play that take into account the spins, iso-spins and symmetry of the wavefunctions.
However, assume I ...
2
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1answer
248 views
Bohr-van Leeuwen theorem and quantum mechanics
Preamble:
If one considers an ideal gas of non interacting charged particles of charge $q$ in a uniform magnetic field $\mathbf{B} = \mathbf{\nabla} \wedge \mathbf{A}$, then the classical partition ...
0
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1answer
89 views
Probabilistic vs Statistical interpretation of Double Slit experiment
Why is it assumed that the results seen in the double slit experiment are probabilistic and not just a statistical result of some unknown variable or set of variables within the system.
3
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0answers
73 views
Semi-conductors
Suppose there is a semiconductor with Fermi energy $E_f$ and that there are $N$ bound electron states.
I'd like to know why the mean number of excited electrons takes the form $$\bar n={N\over ...
0
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1answer
250 views
Pure state - density matrix - real life example of boxes in warehouse
So if there are a billion boxes in a warehouse, I would like to know conceptually how to tell if it is in a pure state.
I know that if it is in a pure state (not mixed) that the density matrix has ...
1
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3answers
515 views
Partition function for quantum harmonic oscillator
Hi guys I'm currently trying to solve a mock exam for an exam in a few days and am a bit confused by the solutions they gave us for this exercise:
Exercise:
A solid is composed of N atoms which ...
7
votes
2answers
343 views
Does chaos theory occur in quantum mechanics? Or in any non-newtonian physics?
Does chaos theory occur in quantum mechanics? Or in any non-newtonian physics? Apart from perhaps thermodynamics?
5
votes
1answer
132 views
Are isolated many-particle quantum systems always in a pure state?
I am trying to understand pure and mixed states better. If I have N quantum particles in an isolated system. The many-particle state is a superposition of the product of single-particle states by the ...
0
votes
2answers
209 views
What are thermal energy distributions?
I am trying to understand the photoelectric-effect deeply. My teacher used the Planck's law and integrated it to deduce the Stefan-Boltzmann law. He somehow showed some quantum-physical ...
1
vote
1answer
592 views
Fermi's Golden Rule and Density of States
I know Fermi's Golden Rule in the form
$$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$
where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition ...
8
votes
3answers
180 views
Is $k_B \rightarrow 0$ the classical limit of stat. mech., as $\hbar \rightarrow 0$ is in QM?
I hear very often among my peers and seniors that just as how $\hbar\rightarrow0$ takes me to classical mechanics from quantum mechanics, $k_B\rightarrow0$ will take me to classical thermodynamics ...
5
votes
1answer
189 views
few fermions in a harmonic trap — position density matrix from diagrammatics
I'm trying to calculate the momentum distribution of a 1D system of non-interacting identical fermions in a harmonic trap.
Given Feynman's answer (from his Statistical Mechanics book) for the ...
0
votes
0answers
56 views
Why is the transition into N proportional to N+1?
I am having trouble understanding the origin of the bosonic stimulated emission. How can I qualitatively understand why bosons Boson's attract each other into similar quantum states.
The furtherst I ...
4
votes
1answer
136 views
How do I calculate the probability that the oscillator is in a certain state using partition function?
So let's say I have a single ($N=1$) quantum harmonic oscillator and the energy is determined by $E_n = (n + 1/2) \cdot \hbar \omega$ (where $n$ is the quantum number and $n$ = $0, 1, 2, \ldots$)
...
4
votes
0answers
246 views
Relating the variance of the current operator to measurements
(EDIT: Thanks to Nathaniel's comments, I have altered the question to reflect the bits that I am still confused about.)
This is a general conceptual question, but for definiteness' sake, imagine a ...
0
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1answer
191 views
Spectrum of quantum fluctuations in a harmonic oscillator
If we have a harmonic oscillator and look at it on small scale the energy is quantized and we can calculate the different eigenstates. In general the energy eigenvalues are given by $$E_n = ...
2
votes
2answers
359 views
The definition of entropy in quantum mechanics
I have seen entropy with several different definitions. Like Von Neumann entropy and Rényi entropy, etc.
So I am curious why there are so many different definitions in quantum mechanics while only ...
6
votes
1answer
135 views
Can closed loops evade the spin-statistic theorem in 3 dimensions?
The famous spin-statistics result asserts that there are only bosons and fermions, and that they have integer and integer-and-a-half spin respectively. In two-dimensional condensed matter systems, ...
1
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1answer
188 views
Simulating quantum network of harmonic oscillators
Let's say that I have a system of $n$ particles $p_1,\ldots,p_n\in\mathbb{R}^3$ (where $n$ here is on the order of 10,000). Furthermore, suppose we have a graph $G=(V,E)$ describing some network, ...
1
vote
2answers
234 views
Confusion about Free Energy and the Hamiltonian
I'm probably making a relatively basic mistake here, but I'm a bit confused about the relation between the Hamiltonian and Helmholtz free energy.
From what I can see, the free energy can be written ...
2
votes
2answers
103 views
Diffusion of probability amplitudes
Let's say I have a probability amplitude $\psi:\Sigma\rightarrow\mathbb{C}$ for some domain $\Sigma$ (so, $\psi$ satisfies $\int_\Sigma |\psi|^2=1$). Is there a way to use $\psi$ as initial ...
1
vote
2answers
95 views
Similarity of probability amplitude functions
Let's say I have two probability amplitude functions given by $\psi_1$ and $\psi_2$. That is, $\psi_i:\Sigma\rightarrow\mathbb{C}$ for some domain $\Sigma$ with $\int_\Sigma|\psi_i|^2=1$ for ...
6
votes
2answers
233 views
Mathematical probabilistic interepretation of probability amplitude
As a warning, I come from an "applied math" background with next to no knowledge of physics. That said, here's my question:
I'm looking at the possibility of using probability amplitude functions to ...
4
votes
3answers
285 views
number of microstates associated with two-level quantum systems
this is a very simple question, but apparently one that has no simple answer, at least from standard quantum mechanics theory
I'm trying to figure the number of simple quantum states (microstates) of ...
6
votes
7answers
471 views
Is it wrong to talk about wave functions of macroscopic bodies?
Does a real macroscopic body, like table, human or a cup permits description as a wave function? When is it possible and when not?
For example in the "Statistical Physics, Part I" by Landau & ...
1
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0answers
82 views
usage of partition function in some number of particles in one-dimensional axis
I just learned some introductory quantum meachnics, but not statistical mechanics, so I am curious how partition functions would be used in the following case:
Suppose there are three particles in ...
5
votes
1answer
380 views
What does the concept of phase space mean in particle physics?
I came across the concept of phase space in statistical mechanics.
How does this concept come about in particle physics?
Why was it introduced and how is it used?
What does it mean when ...
1
vote
1answer
48 views
In which way is decoherence not symmetric between the two considered systems?
If a quantum system interacts with a "big" quantum system, you have dephasing.
The models of decoherence all have this atog aproach to them, about what is to understood of the interaction of the ...
5
votes
7answers
833 views
Is it theoretically possible to reach 0 kelvin?
I'm having a discussion with someone.
I said that it is -even theoretically- impossible to reach 0K, because that would imply that all molecules in the substance would stand perfectly still.
He said ...
2
votes
3answers
163 views
Misconception about the expectation of a quantum system
For a two-level quantum system with energy eigenstates $|\phi_1\rangle$ and $|\phi_2\rangle$ at finite temperature, we can write a general state as ...
1
vote
4answers
229 views
Deriving Statistical Mechanics laws from Quantum Mechanics?
Since the law of individual molecule is governed by Quantum Mechanics, and the interaction of large number of molecule is governed by Statistical Mechanics, can we derive Statistical Mechanics from ...
1
vote
2answers
150 views
Physical Significance for Duality Formula for Entropy
I am studying quantum statistical mechanics from the mathematician's perspective. I don't quite understand what the duality formula for entropy is really saying (or why there is a "duality").
If $A$ ...
5
votes
2answers
91 views
Is ground energy of interacting fermions always higher that that of bosons?
Consider two systems, each made of $N$ particles. In both systems particles interact pairwise and the interaction is given by the same Hamiltonian for both systems. Any other constraints and/or ...
2
votes
0answers
74 views
Factorization of fermionic scattering integral in 2d momentum rep
the scattering integrals for fermions involves both momentum ($k$) and energy ($k^2$) conservation and a nonlinear phase space factor of a distribution function $f(k)$.
$$\begin{multline}I(k) = ...
7
votes
6answers
332 views
How does such strange microscopic behavior at the atomic level (quantum mechanics) lead to the macroscopic behavior at our level?
So, I'm only a high school student researching quantum physics, and I find it very interesting. However, there's one question that keeps nagging at me in the back of my head. How exactly do odd ...
1
vote
1answer
131 views
Quantum Stat-Mech Proof of an Inequality for the Partition Function
I have the following problem that I was unable to solve for class, but I had a couple first steps that I started with that I am unable to finish. I know I can't get this since it's already been ...
5
votes
3answers
487 views
What is the relationship between Schrödinger equation and Boltzmann equation?
The Schrödinger equation in its variants for many particle systems gives the full time evolution of the system. Likewise, the Boltzmann equation is often the starting point in classical gas dynamics.
...
2
votes
1answer
135 views
Infinite quantum well width $L$ to $2L$ adiabatic process
If we change width of the infinite quantum well $L$ to $2L$ slowly enough, how it does change energy levels.
0
votes
2answers
216 views
Reconstruction of information stored in an evaporating black hole from the emission spectrum?
For simple setups, where the radiation field deviates not too far from thermodynamic equilibrium (< 10 %), corrections to the Planckian thermal emission spectrum can be calculated (and measured) ...
1
vote
1answer
174 views
Numerical algorithms to generate a random wavefunction from a thermal ensemble
I am seeking an algorithm to generate a random wavefunction = $\sum {c_i |\varphi _i\rangle }$ from a thermal ensemble, whose density matrix $\rho \sim e^{-\beta H}$, without the need to diagonalize ...
4
votes
1answer
32 views
Connections of iterative solvers for large systems of equation in Physics?
I am trying to find the domains in physics where solving large systems of equations is computationally expensive. The sparse systems are of my particular interest, where the input matrix A is in GBs ...
9
votes
2answers
475 views
Transforming a sum into an integral
I posted this in the mathematical forums. Maybe you will help me. I found an hard article http://prola.aps.org/abstract/PR/v105/i3/p776_1 of yang huang and luttinger. The authors begins with the sum: ...
1
vote
1answer
100 views
Heuristic argument for the temeprature dependence of specific heat in the “low” temperature regimes
Here by "low temperature" I meant it in the scale of the characteristic $\hbar \omega$ of the system.
One can calculate and show that in the low temperature regime $C_V$ of phonons goes like $T^3$ ...
