Unanswered Questions
7,426 questions with no upvoted or accepted answers
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Orbits of maximally entangled mixed states
It is well known (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 each stratum corresponds ...
20
votes
1
answer
492
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What are the exact relations between bound states, discrete spectra, and negative energies in quantum mechanics?
Consider the nonrelativistic quantum mechanics of one particle in one dimension ("NRQMOPOD") with the time-independent Schrodinger equation
$$
\left( -\frac{\hbar^2}{2m} \frac{d^2}{dx^2} + V(...
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18
votes
1
answer
760
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How does one compute the state of a quantum system following imperfect measurement?
Suppose I have a quantum system $S$ ("system") with Hamiltonian $H_S$ and initial density matrix $\rho_S(0)$.
I allow $S$ to interact with another system $P$ ("probe"), which has Hamiltonian $H_P$ and ...
17
votes
2
answers
775
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Is the helium atom with only a contact interaction between the electrons solvable?
Consider the hamiltonian for a helium atom,
$$
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 ...
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16
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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 ...
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15
votes
2
answers
729
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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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14
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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?
- 1,323
12
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Deriving non-relativistic potentials from QFT
Some systems, like atoms, are described well by quantum mechanics, where one just gives the Hamiltonian in the form $H=T+V$ and computes the eigenvalues and eigenvectors of this operator to figure out ...
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11
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1
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Is there a conceptual inverse of anomalies i.e. a notion of quantum enhancement of symmetries?
Anomalies usually occur when a classical symmetry ceases to be a symmetry of the theory when quantized. Are there quantum systems with certain symmetries which cease to exist when you take classical ...
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Is there an AC version of the Quantum Hall Effect?
The quantum Hall effect has the well-known signature of plateaus in the Hall conductivity $\sigma_{xy}=n e^2/h$ that occur at integer values of $n$. This quantization is extremely precise, up to one ...
- 60.3k
11
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View of the sky from inside a black hole
Consider an observer located at radius $r_o$ from a Schwarzschild black hole of radius $r_s$. The observer may be inside the event horizon ($r_o < r_s$).
Suppose the observer receives a light ray ...
- 1,398
11
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Significance for LQG of Sen's result on entropy of black holes?
Sen 2013 says,
...we apply Euclidean gravity to compute logarithmic corrections to the entropy of various non-extremal black holes in different dimensions [...] For Schwarzschild black holes in ...
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11
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1
answer
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Transforming a sum into an integral
I posted this in the mathematical forums. Maybe you will help me. I found an hard article Link of yang huang and luttinger. The authors begins with the sum: $$\frac{{E_2 }}{{E_0 }} = \frac{{16\pi ^2 a^...
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11
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1
answer
457
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Aren't black holes required to exist forever in our frame of reference instead of evaporating?
I know that for an observer far away, nothing ever crosses a black hole horizon (due to time dilation), while in the frame of reference of a falling observer the horizon is nothing special on its way ...
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2
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Why does the Dirac equation work for the hydrogen atom?
The Dirac equation works well for predicting the spectrum of the hydrogen atom, famously incorporating relativistic effects like fine structure. Yet, there seems to be a sense in which this is ...
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