Questions tagged [quantum-mechanics]

Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.

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92
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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 ...
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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 ...
23
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615 views

Uncertainty relation for non-simultaneous observation

Heisenberg's uncertainty relation in the Robertson-Schroedinger formulation is written as, $$\sigma_A^2 \sigma_B^2 \geq \left|\frac{1}{2} \langle\{\hat A, \hat B\}\rangle -\langle \hat A\rangle\...
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742 views

What is the largest number of bosons placed in a BEC?

What is the record for the largest number of bosons placed in a Bose-Einstein condensate? What are the prospects for how high this might get in the future? EDIT: These guys reported 20 million ...
16
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1answer
525 views

Is there a physical interpretation to invariant random matrix ensembles?

Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ...
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Is the converse of Weinberg's statement on the cluster decomposition principle true?

In Weinberg's "The Quantum Theory of Fields, Vol. 1", Section 4.4, page 182, the author says: We now ask, what sort of Hamiltonian will yield an $S$-matrix that satisfies the cluster decomposition ...
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178 views

Why do flux qubits have to be micrometer-sized?

Flux qubits are made using micrometer sized Josephson junctions. They exploit superconducting properties to create and interfere with the magnetic flux between them. My question is that I've seen ...
13
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1answer
806 views

Klein paradox for bosons and fermions

I am reading this paper about the Klein paradox, i.e. transmission of relativistic particles incident on a potential step of height $V_0 > E + mc^2 > 2mc^2$ with $E$ the energy of the incident ...
12
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1answer
847 views

How can I write a Gaussian state as a squeezed, displaced thermal state

I would like to write a Gaussian state with density matrix $\rho$ (single mode) as a squeezed, displaced thermal state: \begin{gather} \rho = \hat{S}(\zeta) \hat{D}(\alpha) \rho_{\bar{n}} \hat{D}^\...
12
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296 views

Topological entanglement entropy only defined for a system in the ground state?

What happens to the topological entanglement entropy of a system, when it is driven out of its groundstate by increasing the temperature?
11
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1answer
199 views

How can one recover the classical frequency-modulation Bessel sidebands from a quantum emitter in a harmonic well?

Consider an atom that emits at frequency $\omega_0$ that's located at a position $x$ that moves under the influence of a harmonic oscillator at frequency $\nu$. In both classical and quantum physics, ...
11
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274 views

How does one compute the state of a quantum system following imperfect measurement?

Suppose I have a quantum system $S$ ("system") with Hamiltonian $H_S$ and initial density matrix $\rho_S(0)$. I allow $S$ to interact with another system $P$ ("probe"), which has Hamiltonian $H_P$ and ...
10
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167 views

Criteria for being able to work with gravity in quantum mechanics, without a full theory of quantum gravity?

It's common to see people oversimplify by saying that physics currently lacks the tools to describe any situation involving both quantum mechanics and gravity. Clearly this is not the case. For ...
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Is the helium atom with only a contact interaction between the electrons solvable?

Consider the hamiltonian for a helium atom, $$ H=\frac12\mathbf p_1^2+\frac12\mathbf p_2^2 - \frac{2}{r_1}-\frac{2}{r_2} + a \, \delta(\mathbf r_1-\mathbf r_2), $$ where I have taken out the ...
10
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1answer
792 views

Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
9
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1answer
152 views

Upper limits for jerk and higher derivatives in physics

Is there an upper limit for jerk in physics? What about higher derivatives? A consequence of special relativity is that no material body can reach or exceed the speed of light in vacuum (due to ...
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99 views

Does the trace distance specify a unique state

In quantum information, we frequently use the trace distance (see definition) to look at how similar two states are. If I had a known complete set of states $\{\rho_i\}$ and some unknown state $\...
9
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136 views

To what extent can one recover plane waves from the Airy eigenfunctions of a linear potential as the field is turned off?

Consider a single massive particle in one dimension under the action of a static linear potential, with the hamiltonian $$ \hat H=\frac{\hat p^2}{2}+\hat{x}F_0. $$ The eigenstate at energy $E$ is, ...
9
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3answers
491 views

How would a realist interpretation of the Mermin-Peres square look like?

How would a realist interpretation of the Mermin-Peres square with counterfactual definiteness and the existence of states prior to measurements look like?
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222 views

Is zitterbewegung physical or not?

It appears that zitterbewegung, a frequency associated with the total energy of a particle or system, is widely considered to be an unphysical quantity (e.g., Kobakhidze et.al.), @Lubos Motl, McMillan)...
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181 views

What happens with the momentum properties of the finite-well eigenstates as the well becomes deeper and deeper?

It's a reasonably standard fact (though not nearly well-known enough) that the momentum operator in the infinite square well is a very problematic beast (as explained e.g. in this and this answers). ...
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334 views

What are problematic issues of quantum field theory in curved spacetime, when accepting semiclassical limitation?

The question is inspired from the answer to Is a QFT in a classical curved spacetime background a self-consistent theory? (I am going to reference this link as "The Q" to avoid confusion). As far as ...
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622 views

Green functions and density matrix

tl;dr The single particle density matrix is directly related to NEGF as shown here, I wish to find a way to relate NEGF also to density matrices which describe probability distribution of many body ...
8
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381 views

Double slit - higher dimensions

The double slit experiment is a real-life manifestation of the Huygens principle. As is well-known, this principle depends on whether the number of dimensions is ever or odd; as Evans1 puts it, ...
8
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659 views

How is conditional probability handled in quantum mechanics?

In ordinary probability theory the conditional probability/likelihood is defined in terms of the join and marginal likelihoods. Specifically, if the joint probability of two variables is $\mathcal{L}(...
8
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1answer
304 views

Computational scaling of quantum and classical Monte Carlo algorithms

How does the computational complexity of finding an equilibrium thermal state for a given Hamiltonian at a given temperature scale with system size under classical and quantum Monte Carlo? I know ...
8
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91 views

How is Mössbauer spectroscopy so resistant to thermal motion?

Mössbauer spectroscopy detects tiny shifts (on the order of $\rm{\mu eV}$ or $\rm{meV}$) in a gamma ray's energy due to the chemical environment of the nucleus. The scan consists of moving a source ...
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411 views

Is there supersymmetry between Dirac and Klein Gordon solutions?

Usually supersymmetry is explained at the level of the action of a quantum field theory, and there are two ways to go down from QFT to relativistic quantum mechanics: either a non-covariant way where ...
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833 views

How to do time evolution of operators in the Heisenberg Picture while staying in the Heisenberg Picture

Consider the time evolution of an operator in the Heisenberg picture: $$\tag{1}i\hbar \frac{d}{d t} \hat{A}_{H}(t) = \left([ \hat{A}_S(t), \hat H_S (t)] + i\hbar \frac{d}{d t} \hat{A}_S(t) \right)_H.$...
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Is the Hilbert space spanned by both bound and continuous hydrogen atom eigenfunctions?

As e.g. Griffiths says (p. 103, Introduction to Quantum Mechanics, 2nd ed.), if a spectrum of a linear operator is continuous, the eigenfunctions are not normalizable, therefore it has no ...
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223 views

Can we have consistent histories inside a black hole?

A consistent history is a POVM set of observables corresponding to a time-ordered product of projection operators. For gauge theories, not any old operator will do, only gauge-invariant observables. ...
7
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160 views

Experimental time-series for quantum particle-in-a-box or simple harmonic oscillator?

I would like to see experimental results for repeated measurement of a single-particle, quantum system that is approximately either particle-in-a-box or simple harmonic oscillator. If particle-in-a-...
7
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94 views

Can the Dirac quantization condition be derived within Lev Vaidman's formalism without gauge fields?

Textbooks often claim that phenomena like the Aharonov-Bohm effect require that any local formulation of quantum gauge theory use gauge potential fields. (It's also sometimes claimed that the A-B ...
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468 views

Is Bohmian mechanics really incompatible with relativity?

This is something I've been wondering about. For those who don't know, Bohmian mechanics is an interpretation of quantum mechanics that is in the class of what are known as "hidden variable theories", ...
7
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138 views

Completely positive maps and symmetric states

Let $\mathcal{N}$ be a completetely positive trace preserving map (aka a quantum channel) acting on a finite dimensional system $\mathrm{A}$, and let $\pi$ denote the maximally mixed state on $\mathrm{...
7
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1answer
527 views

Continuity of Logarithmic derivative in Scattering theory

I have a problem in understanding why we consider the continuity of the Logarithmic derivative of the wave function at the boundary of the Scattering Potential? I understand that physical arguments ...
7
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1answer
475 views

Using open system dynamics to define a quantum state

Background The density matrix of a closed quantum system with Hilbert space $\mathscr H$ evolves according to the von Neumann equation \begin{align*} i\hbar\dot\rho=[H,\rho]. \end{align*} Given a ...
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General formulation for fermions

Let us look at a set of fermionic creation and annihilation operators $b_n$, $b_n^\dagger$ with $n \in \mathbb{N}$. What is the precise relationship between this and this sequence here (partition ...
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What is “spin-orbit torque?”

I am trying really hard to understand the concept of spin-orbit torque. It is a new-ish discovery in the field of spintronics and has many applications for magnetic devices. The information that has ...
7
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Quantum fields from cluster-decomposition principle

I would like help proving Weinberg's claim (I've quoted him below) that quantum fields are an unavoidable consequence of merging particle-based quantum mechanics with both Lorentz invariance and the ...
7
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328 views

Could energy be stored into (not extracted from) the quantum zero point field (like a battery)?

In order to explain the question clearly, I will make a short introduction. In 1962, Josephson predicted that for a sufficiently thin insulating layer, it should be possible for Cooper pairs to ...
7
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2answers
345 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf j_{\...
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$U(N)$ gauged quantum mechanics

I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic? The action I am interested in is $$...
7
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1answer
807 views

Analytical solution of two-level system driving by a sinusoidal potential beyond rotating wave approximation

A quantum mechanical two-level system driven by a constant sinusoidal external potential is very useful in varies areas of physics. Although the widely used rotating-wave approximation (RWA) is very ...
7
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2answers
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Can we solve the particle in an infinite well in QM using creation and annihilation operators?

The particle in an infinite potential well in QM is usually solved by easily solving Schrodinger differential equation. On the other hand particle in the harmonic oscillator oscillator potential can ...
7
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1answer
790 views

Is it possible to construct a quantum “computer” using laser light similar to the double-slit experiment?

Is it possible to construct an arrangement of optical devices (lasers, mirrors, slits, splitters) such that the construction could carry out a single quantum "computation"? I understand that such a ...
7
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1answer
186 views

Quantum Logic and Quantum Field Theory

Quantum Logic is a very interesting and powerful answer to the problem of Quantum Mechanics foundations. Nevertheless this approach is usually developed in a non-relativistic framework. Is it still ...
7
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1answer
192 views

Why alpha particles inestead of hydrogen or duetereum?

I know atoms undergoing alpha decay emit alpha particles, but I was wondering why specifically helium nuclei? If these atoms wanted to emit the smallest unit of matter (I'm talking about hadrons here, ...
6
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Kraus operators for two interacting harmonic oscillators: Problem with the calculation (Ex. 8.21 of Nielsen-Chuang)

I'm working with Exercise 8.21 of the Nielsen-Chuang book on quantum information. It illustrates the amplitude-damping quantum channel by the interaction between two harmonic oscillators (the first ...
6
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1answer
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What does it mean to Fourier transform a ladder operator (in the input-output formalism)?

I am currently trying to get my head around the input-output formalism. In describing the input-output formalism (link) , Gardiner and Collett take ladder operators in the Heisenberg picture and ...