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Apr
25
comment What does the sum of two qubits tell about their correlations?
Will the special case of a pure (but otherwise arbitrarily entangled) composite system be of interest to you.
Apr
22
comment Aharonov-Bohm Effect and Integer Quantum Hall Effect
@ramanujan_dirac, Yes your explanation is correct and conforms with Laughlin's original argument.
Apr
22
comment Aharonov-Bohm Effect and Integer Quantum Hall Effect
@ramanujan_dirac: (cont.) The gauge transformation $\phi$ must be a true function on the circle, i.e. $\phi(0) = \phi(2\pi)$. Thus we can choose a (large i.e., nonhomotopic to the identity) gauge transformation $\phi = n \theta$ to remove the integer part of the flux, such that only its fractional part will enter the Schroedinger equation.
Apr
22
comment Aharonov-Bohm Effect and Integer Quantum Hall Effect
@ramanujan_dirac: The Schroedinger equation a particle moving on a circular ring is invariant under the gauge transformation $\psi\rightarrow e^{i\phi} \psi$, $ A_{\theta }= A_{\theta } + \frac{c \hbar}{eR} \partial_{\theta}\phi$.
Apr
17
comment When can a global symmetry be gauged?
@Tomáš Brauner: Yes, the obstruction to gauging can be understood intuitively by means of the Dirac's constraint theory. If the theory can be gauged, the currents couple to the gauge field. Since the time component of the gauge field is non-dynamical, the charge densities of the symmetry currents will become constraints, i.e., must become zero on the gauge surface which can be thought as a reformulation of the theory with gauge invariant fields. But, then how can the bracket of two vanishing quantities give a nonzero constant.
Apr
17
comment When can a global symmetry be gauged?
Tomáš Brauner: Regarding the remark by drake, Please see section 7.5 of the lecture notes by: Riccardo Rattazzi: itp.epfl.ch/files/content/sites/itp/files/groups/ITP-unit/…. @drake: The scalar Stueckelberg field is real and so is its shifting transformation. The extension to complex values, together with the fact that the Schrodinger Lagrangian is linear in the time derivatives make the shifting transformation anomalous.
Apr
8
comment How does the quantum path integral relate to the quantization of energy?
@drake I have placed a list in a file exchange server: fileconvoy.com/…
Mar
31
comment Aharonov-Casher effect for charged particles
@rubenvb:I have added an update answering your question.
Mar
20
comment Validity of naively computing the de Broglie wavelength of a macroscopic object
@John Rennie You are correct, but I don't know if it is due to the present limitations in knowledge or technology or there is a fundamental theoretical limitation of decoherence. In the first case it might be possible in the future to increase the experimental bounds where interference is observable.
Mar
20
comment Validity of naively computing the de Broglie wavelength of a macroscopic object
Anna cont. It is true that in the composite case the decoherence conditions are harder to achieve, because not only can this system loose coherence by being "kicked" by interacting particles but also it can loose coherence by random excitations of its internal degrees of freedom for example when the thermal excitations exceed its vibrational energies.
Mar
20
comment Validity of naively computing the de Broglie wavelength of a macroscopic object
@Anna cont. When conditions are provided such that the system stays in a single (ground state) internal state, it is possible to approximate it by its center of mass quantum dynamics governed by its de Broglie wavelength, for example in the case of the buckyball and other large molecule interferometry.
Mar
20
comment Validity of naively computing the de Broglie wavelength of a macroscopic object
@Anna What I tried to emphasize is that the de Broglie wavelength is a property of a free degree of freedom. The internal state of the composite system is not free and will not be characterized with its constituents de Broglie wavelengths but rather with its bound state energies for example its vibrational modes.
Mar
20
comment Weyl Ordering Rule
@Ome cont. Please see also the following essay on the subject by Terence Tao: terrytao.wordpress.com/2012/10/07/…
Mar
20
comment Weyl Ordering Rule
@Ome Please see the following concise review: docs.google.com/….
Mar
20
comment Weyl Ordering Rule
@Ome The variables x and k are just dummy integration variables. The integration variables are between minus and plus infinity (This is just a Fourier transform).
Mar
19
comment How to measure a qubit in a random basis
@Niel de Beaudrap The height $z$ is uniformly distributed, $\theta$ is not uniformly distributed. The surface area of all bands $z = z_0\pm\epsilon$ is equal $4 \pi \epsilon$. Please see mathworld.wolfram.com/Zone.html. This is the Archimedes' spherical sampling theorem
Mar
10
comment How does the quantum path integral relate to the quantization of energy?
@drake Please give me a few days, I'll prepare a list.
Mar
9
comment When does $\hbar \rightarrow 0$ provide a valid transition from quantum to classcial mechanics? When and why does it fail?
@stankowait cont. Please, see the following lecture by Daniel Sternheimer on the current status of deformation quantization: guests.mpim-bonn.mpg.de/deform/dsMPIMaugust08.pdf
Mar
9
comment When does $\hbar \rightarrow 0$ provide a valid transition from quantum to classcial mechanics? When and why does it fail?
@stankowait Quantum mechanical amplitudes can be represented by expectations of products of operators. Thus, the star product allows to compute physical amplitudes. It is true that for elementary systems, other quantiation methods are more suitable. However, there are some systems such as moduli spaces and certain infinte dimensional phase spaces of physical interest, where deformation quantization is may be the only available quantization method.
Mar
3
comment Is there a Lagrangian formulation of statistical mechanics?
@Nathaniel. You are correct, the differentials in the Hamilton-Jacobi equation should be with respect to the end point. Also, the time dependence that I wrote is not the most general. In the case of an explicitely time varying Hamiltonian, the phase function depends on $t_0$ and $t_1$ and not only on their difference. In this case the time differetiation is also with respect to the end point. In fact you may choose either one of the boundary points.