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Apr
1
comment A.C. spectrum of the non additive perturbation BAB of a self-adjoint operator A where B is strictly positive
Is this related to anderson localisation ?
Mar
6
answered Does positivity preserve compactness?
Dec
3
comment Fixed point theorems and equiangular lines
@Peter: Can you formulate the conjecture as a fixed point problem ?
Nov
1
comment What is entropy, really?
@Marek : The entropy of a black holes is not zero. Instead it is much greater than the entropy of the star that collapsed to the black hole.
Nov
1
comment What is entropy, really?
Entropy measures our ignorance : It is the logarithm of the phase space volume of macroscopically indistinguishable states. See Roger Penrose, The road to reality, chapter 27.3 .
Oct
16
comment Set of physical states of FQHE on closed Riemann surface = ?
to "set of possible states of that physical system" : That's just the Hilbert space of the quantum system. Furthermore there is no phase transition in FQHE / IQHE (in contrast to superconductivity).
Oct
8
comment Bunimovich stadium bouncing ball
to "probabality distribution of the particles" : There is only 1 particle (the ball).
Oct
1
awarded  Caucus
Aug
23
comment Self-adjointness of a perturbed quantum mechanical Hamiltonian specified in an infinite matrix form
to (2) : you should make this more precise : For instance, there is a divergent series of eigenfunctions of $H_N$ with eigenvalue zero.
Aug
22
comment Ergodic Mean for Schrodinger flow
Your operator acts on the fourier transform $\hat{f}(k)$ as a multiplication by $(e^{-i k^{2}T}-1)/(-i T k^{2})$
Aug
19
awarded  Yearling
Aug
19
comment Ergodic Mean for Schrodinger flow
For a proof use fourier transform or resolution of identity of normal operators. However, I don't know if this is useful for the nonlinear case.
Aug
16
comment C*-algebras and quantum fields
to "Quantum fields have infinitely many degrees of freedom, okay (but only countably many, sorry)" : How do you count them ?
Jul
11
awarded  Nice Answer
Jul
10
answered What is a good method to find random points on the n-sphere when n is large?
Jul
3
comment Why is this operator compact?
I think this is a Hilbert-Schmid-Operator : It's an integral operator with kernel f(x)g(x-y) where g is the fourier transform of $\langle D\rangle^{-n}$ . Hope g is good enough such that this argument works.
Jun
30
comment Quantum mechanics formalism and C*-algebras
If you know the expectation values of all projection operators then you can also calculate the expectation values of the unbounded operators.
Jun
25
awarded  Revival
Jun
1
comment Is the Poincare action on the Klein-Gordon quantum field strongly continuous?
Your argument only shows that the action is not norm continous, and this means that the generators of the group action are unbounded operators.
May
23
comment Is there anyway to rewrite a partial differential equation using language of differential forms, tensors, etc?
An example are maxwells equations, see en.wikipedia.org/wiki/Maxwell%27s_equations.