The research-level tag applies to questions that arise in graduate and post-secondary work. These questions often require domain-specific knowledge and could not be answered from a general source or may be beyond the level typically covered by Wikipedia and other popular sources. research-level ...

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5answers
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What is the use of a Universal-NOT gate?

The universal-NOT gate in quantum computing is an operation which maps every point on the Bloch sphere to its antipodal point (see Buzek et al, Phys. Rev. A 60, R2626–R2629). In general, a single ...
4
votes
1answer
279 views

Does the low-energy gauge structure depend on the choice of $SU(2)$ gauge freedom?

The starting point and notations used here are presented in Two puzzles on the Projective Symmetry Group(PSG)?. As we know, Invariant Gauge Group(IGG) is a normal subgroup of Projective Symmetry ...
2
votes
1answer
30 views

How does negative power lead to amplification?

I am currently investigating semiconductor superlattices and I am analyzing the negative differential velocity (NDV) after a certain limit. I understand how NDV leads to negative power, but I am ...
21
votes
1answer
305 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 ...
0
votes
0answers
13 views

Velocity matrix and non-local pseudo potentials

It is known that velocity of bloch wave functions are related to band energy derivatives: $$v(k)=\frac{1}{\hbar}\frac{\partial \epsilon}{\partial k}$$ However, in the following paper, it is given ...
12
votes
3answers
1k views

Equivalence of definitions of ADM Mass

ADM Mass is a useful measure of a system. It is often defined (Wald 293) $$M_{ADM}=\frac{1}{16\pi} \lim_{r \to \infty} \oint_{s_r} (h_{\mu\nu,\mu}-h_{\mu\mu,\nu})N^{\nu} dA$$ Where $s_r$ is two ...
11
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0answers
337 views

Apparent failure of SUSY nonrenormalization theorem

I am having trouble reconciling two pieces of information. Consider supersymmetric QED, i.e. a supersymmetric U(1) gauge theory with two chiral superfields of opposite charges, $h$ and $\hat{h}$. The ...
1
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1answer
88 views

Global anomaly for discrete groups

We know that: a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
3
votes
2answers
231 views

Does recent paper show Bohmian mechanics is correct?

The following paper was recently featured in a German science magazine (Spektrum der Wissenschaft): "Experimental nonlocal and surreal Bohmian trajectories" (DOI:10.1126/science.1501466) The abstract ...
23
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5answers
5k views

A pedestrian explanation of conformal blocks

I would be very happy if someone could take a stab at conveying what conformal blocks are and how they are used in conformal field theory (CFT). I'm finally getting the glimmerings of understanding ...
1
vote
1answer
42 views

why pseudo wave functions can be used to calculate berry connection

Berry connection plays a very important role in topological insulators. Berry connection $A(k)$ is defined to be $i\langle u(k)|\nabla_k|u(k)\rangle$, where $|u(k)\rangle$ is the periodic part of ...
1
vote
1answer
144 views

Ernst potential from Kaluza-Klein reduction of axisymmetric space-time

Following appendix A of "Ergoregions in Magnetised Black Hole Spacetimes" by G. W. Gibbons, A. H. Mujtaba and C. N. Pope, starting from the Lagrangian $$\mathcal{L} = \hat{R} - ...
12
votes
1answer
448 views

Quasi 1D insulators with strong spin-orbital interaction

We know that the spin-1 chain realizes the Haldane phase which is an example of symmetry protected topological (SPT) phases (ie short-range entangled phases with symmetry). The Haldane phase is ...
7
votes
1answer
264 views

Could the same symmetry be finetuning both the Higgs mass and the inflaton's interactions?

The observed Higgs boson mass is at an interesting place in parameter space, placing the standard model electroweak vacuum right at the edge of metastability. Among the proposed explanations of this ...
5
votes
0answers
92 views

Effective theory of topological insulator in coulomb impurity

I am trying to solve for the Haldane model with a coulomb impurity at one site in the effective theory approach and look for some topology in the solutions of the wave functions. The Hamiltonian near ...
2
votes
3answers
119 views

Gravitational wave detection and electromagnetic counterpart

Background Referring to this article on Fermi EM signal, 0.4 s after the gravitational wave detection by LIGO, FERMI detected an electromagnetic signal (poorly localized) with a false alarm ...
0
votes
1answer
23 views

How is Q-carbon made?

How is Q- carbon made ? https://en.wikipedia.org/wiki/Q-carbon Why a nanosecond laser is needed? How is it cooled ?
6
votes
3answers
2k views

What causes a Phase-Transition?

A phase transition occurs when for example, heat is applied continuously to a liquid and after a certain time it converts into a gas. How does this process work in detail? Is their a chain reaction ...
5
votes
0answers
61 views

Adiabatic turning on of coupling constant in simulation of $\phi^4$ theories in the JLP algorithm

In the Quantum Algorithms for Quantum Field Theories by Jordan, Lee and Preskill they have devised an efficient algorithm to simulate $\phi^4$ theories. Given by the Lagrangian density ...
0
votes
1answer
14 views

Why does natural counting with a gamma spectrometer differ from Neutron activation analysis?

As stated in the title, why are the data from natural counting using s gamma spectrometer different than the data from neutron activation analysis using the same samples?
34
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0answers
957 views

Orbits of maximally entangled mixed states

It is well known (Please, see for example Geometry of quantum states by Bengtsson and Życzkowski ) that the set of $N$-dimensional density matrices is stratified by the adjoint action of $U(N)$, where ...
5
votes
1answer
75 views

Interplay between the cosmological constant and “microscopic” properties of string vacua

As far as I understand, string phenomenology is usually concerned with compactifications of string theory, M-theory or F-theory in which the uncompactified dimensions form a 4-dimensional Minkowski ...
4
votes
0answers
72 views

Are there any open questions in physics that a layman can analyze? [closed]

In math, there are questions like "What is the minimum number of crosses that this knot has?" which can't fundamentally be solved and simply take a lot of trial and error for an answer. This means ...
15
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1answer
2k 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 ...
2
votes
0answers
90 views

The $I_{3322}$ Inequality

I am trying to understand the $I_{3322}$ inequality which is an another example of Bell inequalities and which is different from the famous CHSH inequality. I haven't got hold of any standard ...
10
votes
1answer
789 views

String theory from a mathematical point of view

I have a great interest in the area of string theory, but since I am more focused on mathematics, I was wondering if there is any book out there that covers mathematical aspects of string theory. I ...
6
votes
0answers
173 views

Obtaining the canonical distribution from Fokker-Planck equation?

First I will provide a summary of the problem. Subsequently, I will provide more detail regarding the problem. Please note that entropy is in units of the Boltzmann constant. Summary I have a ...
24
votes
4answers
5k views

Good reading on the Keldysh formalism

I'd like some suggestions for good reading materials on the Keldysh formalism in a condensed matter context. I'm familiar with the imaginary time, coherent state, and path integral formalisms, but ...
16
votes
1answer
544 views

How to evaluate this sum of coupling coefficients?

I would like to evaluate the following summation of Clebsch-Gordan and Wigner 6-j symbols in closed form: $$\sum_{l,m} C_{l_2,m_2,l_1,m_1}^{l,m} C_{\lambda_2,\mu_2,\lambda_1,\mu_1}^{l,m} \left\{ ...
4
votes
0answers
73 views

Gauging a mixture of internal and spacetime symmetries

Given an internal symmetry, say $U(1)$ or $SU(2)$, I understand how to gauge it, by coupling the conserved current $J_{\mu}$ to a gauge field $A^{\mu}$. Similarly, I understand how to gauge a ...
24
votes
4answers
1k views

Regularization of the Casimir effect

For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have ...
46
votes
0answers
2k views

On the Coulomb branch of N=2 supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D $N=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the Casimirs are ...
98
votes
0answers
6k views

Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...
65
votes
0answers
2k views

Experimental test of the non-statisticality theorem?

Context: The paper On the reality of the quantum state (Nature Physics 8, 475–478 (2012) or arXiv:1111.3328) shows under suitable assumptions that the quantum state cannot be interpreted as a ...
39
votes
0answers
1k views

Linear sigma models and integrable systems

I'm a mathematician who recently became very interested in questions related to mathematical physics but somehow, I already have difficulties in penetrating the literature... I'd highly appreciate any ...
8
votes
2answers
1k views

Adiabatic theorem and Berry phase

As far as I can check, the adiabatic theorem in quantum mechanics can be proven exactly when there is no crossing between (pseudo-)time-evolved energy levels. To be a little bit more explicit, one ...
45
votes
11answers
6k views

What is spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
20
votes
4answers
3k views

Wormholes & Time Machines - for *experts* in GR/maths

EDIT: Further clarification in the context of answers/comments received to 20 Jan has been appended EDIT: 21 Jan - Response to the Lubos Expansion appended [in progress, not yet complete] EDIT: 23 ...
21
votes
4answers
1k views

What observables are indicative of BCS Cooper pair condensation?

What observables are indicative of BCS Cooper pair condensation? "Thought" experiments and "numerical" experiments are allowed. This question is motivated by the question Has BCS Cooper pair ...
9
votes
4answers
1k views

Majorana zero mode in quantum field theory

Recently, Majorana zero mode becomes very hot in condensed matter physics. I remember there was a lot of study of fermion zero mode in quantum field theory, where advanced math, such as index ...
3
votes
1answer
475 views

Naive questions on the ground states of Kitaev model

I got some naive questions on the ground states of honeycomb Kitaev model (with open boundary conditions): (1) Consider a simple case that $J_x=J_y=0$, then the model reduces to $$H=J_z\sum_{z\text{ ...
0
votes
0answers
155 views

Alternative expression for Bethe vectors of su(2) XXX chain

As is well known, the eigenvectors of the transfer matrix for the su(2) XXX spin chain of length $L$ are given by acting on the ground state $|\uparrow^L\rangle$ with all spins point up with the ...
8
votes
3answers
1k views

Group Cohomology and Topological Field Theories

I have a two-part question: First and foremost: I have been going through the paper by Dijkgraaf and Witten "Group Cohomology and Topological Field Theories". Here they give a general definition for ...
8
votes
0answers
381 views

How do I enforce the no-slip boundary condition in time dependent incompressible pipe flow?

This is a technical problem which must have been solved already. It won't be in beginners textbooks but there should be a solution somewhere. I welcome reading suggestions. Maybe someone with ...
9
votes
2answers
447 views

What is the algebraic property that corresponds to a topological term?

Warning: This question will be fairly ill-posed. I have spent a lot of time trying to make it better posed without success, so please bear with me. A single $SU(2)$ spin may be represented by the ...
19
votes
2answers
420 views

Geometric picture behind quantum expanders

A $(d,\lambda)$-quantum expander is a distribution $\nu$ over the unitary group $\mathcal{U}(d)$ with the property that: a) $|\mathrm{supp} \ \nu| =d$, b) $\Vert \mathbb{E}_{U \sim \nu} U \otimes ...
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0answers
30 views

Lagrangian for $\mathcal{N}=4$ SQED in 3D

What is the Lagrangian for $3D$ $\mathcal{N}=4$ supersymmetric QED, with $N_f$ hypermultiplets? In particular, which is the form of the Fayet-Iliopulos terms, and the real mass terms?
1
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0answers
30 views

N=4 d=3 susy algebra

Does anybody know how to derive the $\mathcal{N}=4$ d=3 susy algebra doing a dimensional reduction from the most famous $\mathcal{N}=4$ d=4? Equivalently, does it exist a reference in the literature ...
1
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0answers
29 views

The BPS mass formula for 3d N=4

Is the mass formula (or equivalently the central charge formula) known for BPS particles in 3d $\mathcal{N}=4$ susy gauge theories? In particular, what is its dependence on the Fayet-Iliopoulos ...
6
votes
1answer
227 views

What is known about Higgs LHC machine learning algorithm for identifying Higgs events?

Recently many LHC-affiliated organizations and otherwise announced the Higgs ML learning challenge (in May) running over the summer. There are many competing teams and significant results posted ...