Questions tagged [disorder]

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Level statistics of many body localization

I was calculating some Hamiltonian's spectrum statistics. Namely, I calculated the Hamiltonian's eigenvalues and sorted them in an ascending order: $E_1,E_2,E_3...E_N$. The quantity I calculated is r, ...
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19 views

What is a disordered alloy?

I would like some clarification on what is meant by a "disordered alloy." Is this a description of the crystal structure? Is it the same as describing the alloy as amorphous, without a set uniform ...
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175 views

What is the intuition behind the statement that non-equilibrium systems with static disorder are self-averaging?

In this paper(1) by C. De Dominics, he makes the argument that in a dynamical statistical mechanics system, one doesn't need to apply the replica trick and can directly disorder average the generating ...
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If universe is expanding shouldn't its 'disorderness' decrease?

I've came across Clausius Inequality which says that entropy of an isolated system always increases (in an irreversible process). Assuming universe to be an isolated system, a time will come when ...
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89 views

Calculate an order parameter for a given set of atomic coordinates

I have a box which contains a few thousand atoms, and I would like to be able to calculate a single number which gives some indication of how ordered their arrangement is in 3D. For example, if they ...
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2answers
216 views

What is(are) the effect(s) of disorder on electrical conductivity?

As a non-specialist, I asked the question "What are disorders in condensed matter parlance?" about the meaning of disorder in condensed matter physics. I also wrote a non-specialist answer after some ...
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1answer
189 views

What are disorders in condensed matter parlance?

Condensed matter physicists often use the term disorder. What is a disorder? Is it some point defect or line defect? How are they modelled in a theory?
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269 views

Why do we disorder-average before/after taking the logarithm of the partition function for annealed/quenched disorder?

Pg. 19 of these notes says Crucially, the [disorder] average $\overline{\log Z}$ has to be computed after taking the logarithm. Such an average is called quenched ... Computing the average first, ...
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208 views

Difference between Anderson localization and weak localization

I have read that weak localization is a precursor to Anderson localization. Weak localization happens due to the constructive interference between paths that loop around in opposite direction, on ...
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140 views

Derivation of the gradient expansion of the Keldysh nonlinear sigma model for disorder metals

My confusion relates to Appendix C of this this paper although the same derivation is presented in many others. When deriving the gradient expansion of this term arrives at a term quadratic in the ...
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1answer
51 views

Are maximum order and maximum disorder equally easy to describe?

If we have a collection of particles in a maximum ordered state, is this state just as easy to describe as a collection of particles in a minimum ordered state? If we have a collection of particles ...
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3answers
631 views

What does the second law of thermodynamics really mean?

I started reading about entropy and the second law of thermodynamics. Different sites give different definitions and meanings of this law. A few of them: Disorder always increases heat always flows ...
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1answer
147 views

Fractal structure in colloidal systems

In describing the configuration of a colloidal system, one often deals with either, disordered fluid states, disordered jammed states or crystalline states (so an underlying lattice structure), but in ...
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1answer
580 views

Quenched systems - disorder average (SYK model)

In a system with quenched disorder one is usually looking for self-averaging quantities, i.e., quantities such that the average over the couplings produces a ``typical" configuration in the ...
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45 views

Single-electron propagator in disordered media: higher moments?

The known result that the impurity-averaged single electron propagator takes the form $ \langle G_0(r) \rangle \sim e^{-|r|/\ell} $, for $\ell$ the mean free path is frequently quoted by papers on ...
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46 views

Superconductor-insulator transition at finite temperatures

I know that it is possible to have a phase transition at $T=0$ between a superconductor and an insulator. The mechanism is not the "usual" QPT as the system is not translationally invariant: the ...
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157 views

Do hydroelectric power plants violate the popular scientific notion of entropy = disorder?

I had a discussion yesterday, and I found my understanding of entropy lacking. I know that entropy is not exactly the same as the degree of disorder in a system, but I also know that outside of ...
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1answer
172 views

Why does entropy arise from order?

Why does entropy arise from order? Thanks. I'm not sure if this question has already been answered on this site. If anyone needs me to clarify the question, please post in the comments and I'll ...
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2answers
686 views

Difference Between Ruderman-Kittel-Kasuya-Yosida (RKKY) Interaction and Kondo Effect

The question is in the title. I don't understand the difference between these two effects. Based on my understanding, the Kondo Effect is where the conduction electrons effectively screen a local ...
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55 views

What is a zero temperature horizon?

While reading the paper "Disorder horizons: Holography of randomly disordered fixed points" by Hartnoll and Santos, I came across this: We are interested in solutions with a zero temperature ...
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1answer
40 views

Conductance of disordered conductor

I'm struggling with a rather advanced problem. Consider a conductor placed between two leads. The conductor is not completely clean but contains all kinds of impurities. The goal is to find the ...
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1answer
707 views

Physical understanding of Anderson (disorder) localisation

My current understanding is that waves in disordered potentials experience localisation due to interference effects. (eg an electron in a disordered medium tries to take different paths of effectively ...
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210 views

Why doesn't entropy get decreased in adiabatic expansion process?

I was reading the second step of Carnot cycle in which the system undergoes adiabatic expansion doing work & thus decreasing the internal energy of itself. The entropy didn't change as no further ...
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72 views

phonon dispersion with random masses

In order to see how phonons should be affected by disorder, I've been playing around with a model involving a 1D chain of masses linked by springs, where the spring strengths are all the same but the ...
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2answers
722 views

scaling theory of Anderson localization

Initially, Anderson studied the eigenstates of the tight-binding Hamiltonian $$ H = \sum_n \epsilon_n a_n^\dagger a_n + V \sum_{m,n} a_m^\dagger a_n . $$ His question was whether the eigenstates ...
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1answer
241 views

Why does the diffusion pole universally appear in the two-particle Greens function (diffuson)

I've been thinking about the calculation of the diffuson in the context of impurity-averaged Greens functions. If you calculate the two-particle Greens function in the ladder approximation (for ...
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2answers
200 views

Entropy / Structure Relations

I want to check on the validity of the following objective definition of order. Is it correct? Is there a more rigorous statement of this concept? The further a system is from its maximum ...
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1answer
97 views

Orienational order parameter in isotropic systems

I have what may be a dummy question. In NMR or in the study of liquid crystals for example, an order parameter $S$ is often used: $$ S=\left\langle\frac{1}{2}\left(3\cos^2\theta−1\right)\right\rangle $...
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76 views

Maximising entropy when energy is shared between systems

This is a problem to do with statistical physics, and the exchange of energy when we have two microcanonical ensemble. I don't understand why there should be a minus sign in the middle, if Energy* is ...
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2answers
100 views

Modeling a list with a tunable degree of disorder/shuffling

Imagine we have a list of ordered numbers $L = (1, 2,\dots, N)$. I want to add an arbitrary amount of "disorder" to that list. For instance: Adding a little bit of disorder would permute a few ...
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1answer
354 views

Confusions regarding entropy

Help, I am terribly confused about entropy. On the one hand, I am taught at school that a substance such as an ice/solid has a lower entropy than its gaseous equivalent and that a process such as ...
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2answers
263 views

Qualitative discussion about entropy and disorder

Many discussions about entropy and disorder use examples of decks of cards, pages of books thrown in the air, two gases being mixed in a container, even the state of a nursery at the end of the day ...
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63 views

Random quantum systems with asymmetric Lifshitz tails?

For a quantum mechanical system with a periodic Hamiltonian (Schrödinger operator) $H$, let $N(E)$ be its integrated density of states, i.e. the fraction of eigenvalues in the spectrum $\sigma(H)$ ...
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388 views

Entropy: two explanations for the same quantity?

I studied thermodynamics and I saw the following definition for entropy: $$ \Delta S = \int_1^2 \frac{\text{d}Q}{T} $$ that we use to calculate $\Delta S$ for different types of transformations. In ...
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136 views

Qualitative argument to determine energy of defects

In a book of "LES HOUCHES - Critical Phenomena, Random systems, Gauge theories" the author Frolich says that: 2D In two dimensions, the mean energy of an isolated point defect in a square area of ...
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1k views

Interpretation of the Random Schrödinger Equation

I should preface this by admitting that my physics background is rather weak so I beg you to keep that in mind in your responses. I work in mathematics (specifically probability theory) and a paper ...
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70 views

finding resistance from percolation theory with only energy disorder

Within an Miller-Abrahams random resistor model, finding the critical resistance when there is spatial disorder is simple as there is the bonding criterion $\int_0^{r_c} 4 \pi N r^2 dr = B_c \approx ...