# All Questions

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### Frequency of flute note heard using Doppler effect when both the source and observer are moving

Let us consider this scenario. A bicycle rider and a flute player are moving in the same direction at speeds 36 km/h and 18 km/h. The flute is producing a note of frequency 600 Hz. We need to find ...
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### Is getting the ground state of Edwards-Anderson model NP hard?

I know 1D and 2D Ising model has a general solution. And I also know getting the ground state of 2D Ising model with transverse field and 3D Ising model is NP-hard.[Onsager][Barahona] So my question ...
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### Can we use combined symmetry to simplify the calculation of algebraic PSGs?

In classifying mean-field spin liquids under projective construction, the algebraic projective symmetry group (PSG) approach focus on the mathematical construction of the possible extensions of the ...
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### Reason behind formation of doublets in diffraction spectrum

like if you see is Sodium (and also in Mercury), there are two discrete lines of Yellow color.. What's the reason behind formation of doublets?
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### Ising Monte-Carlo and Three point functions

I'm looking for literature on the calculation of three points function in the 2d Ising Model using numerical methods, especially around the critical point. By $Z_2$ symmetry, three spin insertions is ...
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### Interpretation of Dirac Spinor components in Chiral Representation?

I failed to find any book or pdf that explains clearly how we can interpret the different components of a Dirac spinor in the chiral representation and I'm starting to get somewhat desperate. This is ...
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### Do all the spacelike curve terminate at the spatial infinity $i_0$ in the Penrose Diagram of a Schwarzchild black hole?

Let's restrict to the radial direction, so the metric can be expressed as $ds^2=-(1-r_S/r)dt^2+(1-r_S/r)^{-1}dr^2$ with $r_S$ the Schwarzchild radius. Expressed in Kruskal coordinates, the metric is ...
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### space representation of a local potential

Why is it that for a local potential $V$: $$\langle x | V | x' \rangle = V(x) \langle x | x' \rangle = V(x) \delta(x - x')$$ I saw this being used in a book but without any explanation. The part with ...
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Please look at the following link for the sketch of the problem: Adiabatic Expansion with expanding control volume I have a certain amount of gas at a certain pressure and temperature at the start. ...
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### Zeta regularization for a series and an integral

Given the UV divergence $$\int_{0}^{\infty}dx$$ in order to regularize it, I introduce a regulator $|x|^{-s}$, so I have $$\int_{0}^{\infty}x^{-s}dx$$ My problem and doubt is how can I relate ...
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### What does it mean to charge a length of wire up to potential v?

I have to study the text "On the Theory of the Electric Telegraph," By William Thomson, 1855. I am having trouble gaining a conceptual understanding of the opening: "Let c be the electro-statical ...
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### Kinetic energy of the spring

Suppose we have spring of mass $m$ initially at rest , now instantaneous velocity of $v$ is given at both ends in opposite direction (nothing is attached to spring) so what will be kinetic energy of ...
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### Can the granular quantum nature of light be used to engineer a maroscopic optical phenomena?

Today we have optical metamaterials and metasurfaces: materials and surfaces that are made of unit cells with an approximate size of tens of nanometers, that can that interact with light and can have ...
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### Relating Angles in Elliptical Orbit

I've been trying to model the orbit of a comet of arbitrary mass around our sun from having a known initial condition with $r_0, v_0$ with angle $\alpha$ at $t_0$ around our sun. I've been able to ...
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### Simplified calculation to find Lagrange point L1

I'm trying to find the position of Lagrange point L1 in the earth-moon system. To make the whole thing easier (I thought) I don't care about the sun's influence or any other forces than the ...
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### what happen if we have a set of divergent constant $a_{n}$ but in our theory we have only the $m$ mass and the coupling constant?

Let us suppose we have 4 divergent integrals: $$\int_{0}^{\infty}x^{m}dx = u_{m},\ \ \ \ \ \ \ \ \ m=0,1,2,3$$ but our only free parameters are the $m$ mass and $q$ charge. Can we 'invent' two ...
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### Retarded Green function and the gravitational field of a point particle

I'm trying to understand a calculation by Aichelburg and Sexl of the gravitational field of a point particle. Linearizing the Einstein field equations in the usual way (that is, supposing a metric of ...
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### Is the gravitational acceleration at the event horizon constant?

If the escape velocity at the event horizon of a black hole is equal to the speed of light, does this imply that the gravitational acceleration at the event horizon is also constant? For example, ...
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### $2\to3$ Phase space Integration

I have a $2\to3$ process ($P=p_1+p_2 \to p_3+p_4+p_5$) where all particles in the initial state and one of the particles in the final state ($p_3$) are massless. The other two ($p_4$ and $p_5$) have ...
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### In thermodynamic identity, dU=TdS-PdV. Are dS and dV orthogonal or is (T,P) defined in a conjugated space from (dS,dV)?

In thermodynamic identity, we say dU=TdS-pdV, and only Maxwell's relation is required for U to be a proper behaved thermodynamics variable. But from multivariable calculus, that result requires dS ...
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### Does the surface topological order on the boundary of 3D topological insulator also have topological ground state degeneracy?

The boundary of a 3D topological insulator can be fully gapped (under strong interaction) by the surface topological order without breaking the symmetry (see Fidkowski-Chen-Vishwanath, ...
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### Converting between cosmological times

David Hogg's 'Distance Measures in Cosmology' is my go-to reference for all things cosmological. It's missing a discussion of time measurements however. How does one convert between different ...
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### Crystal in Magnetic Field

When you have a 2D crystal in a uniform perpendicular magnetic field, you can use the Peierls substitution to convert one tight-binding before-magnetic-field-band into a $q$-bands under the influence ...
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### Hamiltonian symmetry Lie algebra

What is the connection between complete set of commuting observables and generators of the Lie group? I have a Hamiltonian written down in second quantized formalism and I also checked that it ...
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### Binding forces in crystalline solids

I am referring to rocks in this instance. Individual crystals grow together in an igneous rock as it solidifies. I know that the SiO4 tetrahedron is the basic building unit of silicate minerals, and ...
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### Create a transmission protocol to transfer both data and energy(Wireless Communication)

Is there a protocol by which we can design systems that jointly transfer both data and energy ? Some kind of gadget that collects the received energy, temporarily stores it in a battery and later uses ...
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### Extracting something from Schwarzschild metric

In Papapertrou's lecture book on General Relativity he said in p 137 that from the metric $$ds^2= e^\nu dt^2-e^\mu dr^2 -r^2(d\theta^2 +\sin^2\theta d\phi^2)$$ one deduces that \sqrt{-g} ...
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### How is 2D spectroscopy able to show quantum coherent transport through networks?

For wave-like (quantum coherent) energy transfer in networks (eg. propagation of excitation in photosynthetic protein complexes of algae or FMO complex in plants) 2D electronic (photon echo?) ...
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### Raman amplification

Recently I read a bit about Raman amplification. Unfortunately, I did not understand everything. As far as I understood the resulting wavelength only depends on the pumping wavelength. Now I heard on ...
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### Coupling a ferromagnet to an antiferromagnet

Consider a system composed of a thin film of FM material on top of an AFM material. From my research I found that pinning of the FM material occurs when we cool the system from $T_N<T<T_C$ to ...
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### Chemical potential related with quantum and classical limit in ideal gas

For ideal gas we have chemical potential $\mu = \tau \ln \left(\frac{n}{n_Q}\right)$ where $n = N/V$ number density and $n_Q = \left(\frac{M\tau}{2\pi \hbar^2}\right)^{\frac{3}{2}}$ Note we call ...
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### Does non-rotating object have rotational inertia if it is attach to rotating object by a spring

My question relating to the Rotational Inertia as a whole system. As I learn that the Rotational Inertia is defined for a rotating object to an fixed axis but I got problem in the case a rotating ...
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### Rationale for definition of input/output operators in quantum langevin equations

I am going through Gardiner & Zoller's 'Quantum Noise', and following the derivation of the Langevin equations in terms of input/output operators. Let the bath Hamiltonian be: ...
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### Adiabatic Relation in Plasma Invariant and Thermodynamics

In the problem above, I know how to do the 1D part. Basically, you just plug $V_{l\,l} = \frac{J}{L}$ into $\langle \frac{1}{2} m v^2\rangle = \frac{1}{2} k T$. After you get $T$ in terms of $L$, ...
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### Can “uniform motion” (or “mutual rest”) be determined intrinsically, by members of Synge's “five-point curvature detector”?

In his description of a "five-point curvature detector" [1], J. L. Synge exhibits a Cayley-Menger determinant in terms of "optical distances" between five distinct participants; and he states that the ...
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### Is this Process Possible?

An inventor has devised a complicated non-flow process in which 1 mol of air is the working fluid. The net effects of the process are claimed to be: A change in state of air from 250$^{\circ}$C and ...
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### Lasers without Population inversion?

When I made a study on lasers, I found a webpage saying that the quantum mechanical principles enable us to create laser action without population inversion, which Einstein suggested as one of the ...
### Is it OK to see time dilation and (relativistic) mass increase as phenomena that avoid $c$ being reached? And how about length contraction?
I think I have been exposed since years ago to this line of reasoning: if $v\to c$, then $\Delta t \to \infty$. As $\displaystyle v=\frac{\Delta s}{\Delta t}$, it's like a natural reaction to ...