Tagged Questions

The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.

learn more… | top users | synonyms

2
votes
1answer
232 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.
-3
votes
2answers
321 views

Occam's razor on spin statistics theorem?

Highly related to A reading list to build up to the spin statistics theorem I see 2 parts to the spin statistics theorem: (spin $n$ or $n+\frac{1}{2}$) step 1 given that a spin is integral or ...
3
votes
2answers
506 views

Axiomatic statistical mechanics

Ive read a few courses on statistical mechanics, and while their textual explanations and example choices differ, the flow of information from microscopy to macroscopy seems the same, and reading ...
4
votes
1answer
296 views

What are conditions for the existence of a critical value (for a phase transition)?

Can there only be a critical temperature if there is some natural unit for an observable in the model, i.e. if there is a natural scale for something? Otherwise I don't see how for a system there ...
2
votes
3answers
226 views

How to “read” the temperature of an abstract system?

How can I interpret the parameter temperature $T$, if I'm not given the description of the system in terms of the equation of state, $E(S,V\ )$ or $S(E,V\ )$ and so on. In many systems it makes sense ...
4
votes
0answers
273 views

Stability of the vacuum state of interacting quantum fields

"Stability" is generally taken to be the justification for requiring that the spectrum of the Hamiltonian should be bounded below. The spectrum of the Hamiltonian is not bounded below for thermal ...
3
votes
1answer
219 views

From spectrum/dispersion relation to the partition function

I know the spectrum/dispersion relation for a bosonic system. $$E \left( \mathbf{k} \right) = \cdots$$ Is there a general method for writing down the partition function when the spectrum of the ...
7
votes
0answers
284 views

Information geometry of 1D Ising model in complex magnetic field regime

Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by $$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
6
votes
2answers
263 views

Renyi entropy in physical systems

We know that the Shannon entropy $H(P)=- k_{\mathrm{B}}\sum_i p_i \ln p_i$ is mostly the entropy of the thermodynamic systems. Does the Renyi measure $H_{\alpha}(P)=\frac{1}{1-\alpha}\log \sum ...
6
votes
1answer
321 views

What is the information geometry of 1D Ising model for a complex magnetic field?

Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by $$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
3
votes
2answers
808 views

Can a system entirely of photons be a Bose-Einsten condensate?

Background: In Bose-Einstein stats the quantum concentration $N_q$ (particles per volume) is proportional to the total mass M of the system: $$ N_q = (M k T/2 \pi \hbar^2)^{3/2} $$ where k ...
1
vote
2answers
252 views

Polarisation directions in standing waves in cubical cavity

I was studying Rayleigh-Jean's formula. The author has assumed a cubical cavity of each side $L$ with perfectly reflecting surfaces. According to author, there are two perpendicular directions of ...
8
votes
5answers
4k views

Why was the universe in a extraordinarily low-entropy state right after the big bang?

Let me start by saying that I have no scientific background whatsoever. I am very interested in science though and I'm currently enjoying Brian Greene's The Fabric of the Cosmos. I'm at chapter 7 and ...
8
votes
2answers
4k views

How to derive Fermi-Dirac and Bose-Einstein distribution using canonical ensemble?

My textbook says that microcanonical ensemble, canonical ensemble and grand canonical ensemble are essentially equivalent under thermodynamic limit. It also derives Fermi-Dirac and Bose-Einstein ...
4
votes
3answers
1k views

How to understand temperatures of different degrees of freedom?

So I'm reading this book, where after the preface and before the models there is a section called General Notions and Essential Quantities, which introduce some things I don't understand. They regard ...
1
vote
2answers
246 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) ...
9
votes
1answer
67 views

Renyi fractal dimension $D_q$ for non-trivial $q$

For a probability distribution $P$, Renyi fractal dimension is defined as $$D_q = \lim_{\epsilon\rightarrow 0} \frac{R_q(P_\epsilon)}{\log(1/\epsilon)},$$ where $R_q$ is Renyi entropy of order $q$ ...
6
votes
5answers
437 views

Theoretical proof forbidding Loschmidt reversal?

In a famous debate, Loschmidt criticized Boltzmann's new theory of statistical mechanics by asking what would happen if the velocities of all the atoms were reversed. Typical objections are that such ...
1
vote
1answer
254 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 ...
10
votes
0answers
82 views

Quantum statistics of branes

Quantum statistics of particles (bosons, fermions, anyons) arises due to the possible topologies of curves in D-dimensional spacetime winding around each other What happens if we replace particles by ...
1
vote
1answer
147 views

Renormalization Group for anisotropic “Gaussian” model

I'm considering an "anisotropic" Hamiltonian of the form $$\beta H = \int d^n r_{||} d^{d-n} r_{\bot} \frac{K}{2} (\nabla_{||} m)^2 + \frac{L}{2} (\nabla^2_\bot m)^2 + \frac{t}{2}m^2 - hm$$ which in ...
4
votes
1answer
320 views

Renormalization Group: Different fixed points

Extending the Gaussian model by introducing a second field and coupling it to the other field, I consider the Hamiltonian $$\beta H = \frac{1}{(2\pi)^d} \int_0^\Lambda d^d q \frac{t + Kq^2}{2} ...
0
votes
2answers
243 views

RG of the Gaussian Model: Finding the scaling factor

I'm studying how the Renormalization Group treatment of the simple Gaussian model, $$\beta H = \int d^d r \left[ \frac{t}{2} m^2(r) + \frac{K}{2}|\nabla m|^2 - hm(r)\right]$$ In momentum space, the ...
1
vote
2answers
412 views

How do derive this result in stat-mech style

I'm going through (well, at least I'm planning to) Rief's book about statistical mechanic (I want to improve my knowledge). I want to be serious about this so I'm trying to solve as much problem as I ...
5
votes
3answers
869 views

canonical and microcanonical ensemble

What does one mean by canonical and micro canonical ensemble in statistical mechanics? Can one elaborate on this in a very simple way with examples? Pardon me, if it is a very simple thing; I am a ...
1
vote
1answer
140 views

On BE and FD Statistics

Lets consider the Bose-Einstein and Fermi-Dirac statistics: Bose-Einstein statistics: $$\langle n_i\rangle = \frac{1}{\exp{[(\epsilon_i-\mu)/kT]} - 1}$$ Fermi-Dirac statistics: $$\langle ...
6
votes
1answer
361 views

Motivation for maximum Renyi/Tsallis entropy

The Conditional limit theorem of Van Campenhout and Cover gives a physical reason for maximizing (Shannon) entropy. Nowadays, in statistical mechanics, people talk about maximum Renyi/Tsallis entropy ...
3
votes
1answer
124 views

Definition regarding percolation

in a homework sheet studying bond-percolation on the Bethe lattice, a function $g(r)$ is introduced as "the probability of finding two nodes separated by a distance $r$ on the same cluster". Now ...
3
votes
1answer
789 views

Calculating the heat capacity of a system

I have started reading Statistical Physics by F. Mandl and I would appreciate some help with the following exercise A system consists of $N$ weakly interacting subsystems. Each subsystem possesses ...
2
votes
3answers
464 views

Should annealed disorder be characterized by the average of the partition function?

Most of the literature says that for a quenched average over disorder, an average over the log of the partition function must be taken: \begin{equation} \langle \log Z \rangle, \end{equation} while ...
6
votes
4answers
788 views

Partition Function as characteristic function of energy?

I'm going through a book on statistical mechanics and there it says that the partition function $$Z = \sum_{\mu_S} e^{-\beta H(\mu_S)}$$ where $\mu_S$ denotes a microstate of the system and $H(\mu_S)$ ...
12
votes
1answer
442 views

What are some predictions from string theory that say some crystalline materials “will end up in one of many lowest-energy ground states?”

I am referring to this recent "news feature" by Zeeya Merali from Nature magazine www.nature.com/uidfinder/10.1038/478302a. Here is the specific quote: "To make matters worse, some of the testable ...
6
votes
2answers
474 views

Analogue of Princeton Companion to Mathematics for Physics?

I would like to know if there are compendiums much like the Princeton Companion to Mathematics for physics (especially classical physics: fluid mechanics, elasticity theory, Hamiltonian formalism of ...
15
votes
4answers
436 views

What is a simple intuitive way to see the relation between imaginary time (periodic) and temperature relation?

I guess I never had a proper physical intuition on, for example, the "KMS condition". I have an undergraduate student who studies calculation of Hawking temperature using the Euclidean path integral ...
4
votes
1answer
38 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 ...
4
votes
1answer
943 views

Infinite-range 1D Ising model + Hubbard-Stratonovich-Transformation

I have a probably quite simple question RE the HST. After some work, I obtain as the partition function for the infinite range 1D Ising model $$Z = \int_{-\infty}^\infty \frac{dy}{\sqrt{2\pi / ...
8
votes
3answers
346 views

Can the Metropolis-Hastings algorithm be generalized to quantum systems?

The Metropolis-Hastings algorithm is an efficient way of simulating classical ensembles using the Monte Carlo method. Is there a generalization of this algorithm to quantum systems? What I DON'T have ...
26
votes
5answers
696 views

What are some critiques of Jaynes' approach to statistical mechanics?

Suggested here: What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis? I was wondering about good critiques of Jaynes' approach to statistical ...
16
votes
1answer
166 views

Fluctuations of an interface with hammock potential

This question is related to that one. I ask it here since comments are too short for the extended discussion that was going on there. I am interested in a very simple interface model. To each ...
7
votes
1answer
122 views

Canonical averages in a Fermi gas aka generalized Fermi-Dirac distribution

I am in the process of applying Beenakker's tunneling master equation theory of quantum dots (with some generalizations) to some problems of non-adiabatic charge pumping. As a part of this work I ...
14
votes
1answer
137 views

Phase Transition in the Ising Model with Non-Uniform Magnetic Field

Consider the Ferromagnetic Ising Model ($J>0$) on the lattice $\mathbb{Z}^2$ with the Hamiltonian with boundary condition $\omega\in\{-1,1\}$ formally given by $$ ...
26
votes
0answers
253 views

Systematic approach to deriving equations of collective field theory to any order

The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
14
votes
2answers
57 views

Sampling typical clusters between distant points in subcritical percolation

I have on several occasions wondered how one might proceed in order to sample large subcritical Bernoulli bond-percolation clusters, say on the square lattice. More precisely, let's consider the ...
1
vote
0answers
191 views

What does it mean for a phase space trajectory to be “long” and “stable”?

What does it mean for a phase space trajectory to be "long" and "stable"? I understand the concept of a trajectory in phase space but not how these adjectives can be applied to one. Thanks.
14
votes
1answer
981 views

Onsager's Regression Hypothesis, Explained and Demonstrated

Onsager's 1931 regression hypothesis asserts that “…the average regression of fluctuations will obey the same laws as the corresponding macroscopic irreversible process". (Here is the links to ...
0
votes
1answer
142 views

Use of escort distribution in nonextensive stat. mech

In some of the articles which I read recently, I happen to see the following statement. In Nonextensive statistical physics, it is inappropriate to use the original distribution $P=(p_i)$ ...
20
votes
5answers
170 views

Connections and applications of SLE in physics

In probability theory, the Schramm–Loewner evolution, also known as stochastic Loewner evolution or SLE, is a conformally invariant stochastic process. It is a family of random planar curves that are ...
2
votes
0answers
220 views

How is the “negative dispersion” derived?

I'm looking at Kopfermann H., Ladenburg R., Nature, 122, 338-339 (1928) and it appears Ladenburg in Ladenburg R., Z.Physik, 4, 451-468 (1921) was the first to discover the phenomenon of "negative ...
22
votes
1answer
385 views

Mermin-Wagner theorem in the presence of hard-core interactions

It seems quite common in the theoretical physics literature to see applications of the "Mermin-Wagner theorem" (see wikipedia or scholarpedia for some limited background) to systems with hard-core ...
6
votes
1answer
210 views

Nonextensive statistical mechanics

I know that the Tsallis($S_q$) entropy is called nonextensive information measure in the sense that if $P$ and $Q$ are two probability distributions then $S_q(P\times ...