1
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0answers
43 views

Time evolution operator of a periodic Hamiltonian

Suppose we have a Hamiltonian $H(t)$ with periodicity $T$. The time evolution operator in a full period is $$U_1=\cal{T}e^{-i\int_0^T H(t)\mathrm{d}t}$$, where $\cal{T}$ is time ordering operator; ...
2
votes
0answers
24 views

Detailed Balance for Quantum Master Equations from System Hamiltonians with Degenerate Spectrum

Kossakowski, Andrzej, et al. ("Quantum detailed balance and KMS condition." Communications in Mathematical Physics 57.2 (1977): 97-110) gave a proof that the stationary state of a quantum dynamical ...
0
votes
3answers
48 views

Is a gapless system always conducting and a gapped system insulating?

In an answer to this question, @user566 mentioned that there is a qualitative difference between gapped and gapless systems; that gapless systems are conducting and gapped system are insulating. Is ...
1
vote
1answer
231 views

Non-trivial solution for a linear set of coefficients involved in the phonon modes of a semiconductor quantum dot

I am trying to use the method outlined in this linked paper (T. Takagahara, Journal of Luminescence, 70 (1996), pp. 129-143) to find the phonon-exciton coupling in a spherical PbS quantum dot. In Eq ...
0
votes
1answer
35 views

compressibility of cold atoms in optical lattices

The compressibility of cold bosons in an optical lattice is defined as $\kappa = \frac{\partial \langle n\rangle}{\partial \mu}$, where $\langle n\rangle$ is the density and $\mu$ is the chemical ...
4
votes
0answers
115 views

Eigenvalue of the adiabatic Hamiltonian of Farhi's three qubit 2-SAT problem

I was trying to reproduce example 3.3 of Quantum Computation by Adiabatic Evolution by Edward Farhi et. al. This is an adiabatic algorithm to solve an instance of three qubits 2-SAT problem. I think ...
2
votes
2answers
77 views

Optical absorption in a semiconductor for $E<E_g$ [duplicate]

Quoting from Solid State Electronic Devices (by Ben G. Streetman and Sanjay Banerjee): A photon with energy less than $E_g$ is unable to excite an electron from the valence band to the ...
1
vote
0answers
83 views

Energy of an Electron in a One Dimensional Periodic Potential

First, we consider the time independent Schrodinger equation of the form: $$\bigg(-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+u(x) \bigg)\phi_A(x)=E_A\phi_A(x)$$ Where $u(x)$ is a potential created by a ...
2
votes
0answers
36 views

Energy from the Feynman-Kikuchi Partition Function

The Feynman-Kikuchi Partition function is given as $$Z_{FK}=K_\beta \int dx \eta(x) \exp \left(-\frac{x}{\beta}\right) $$ where $K_\beta$ is a normalization constant and ...
5
votes
0answers
77 views

Why do people say “Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon).”?

Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon, etc.). I read this in a paper (version1 of http://arxiv.org/abs/1404.3728v1, 1st page 1st ...
4
votes
0answers
35 views

How to distinguish Bose glass and superfluid phases in a harmonic trap?

In mean-field study of Bose-Hubbard model in an optical lattice, what parameter can be calculated to distinguish Bose glass and superfluid in a harmonic trap?
0
votes
0answers
18 views

Condensate fraction and momentum distribution in cold atom experiments

In ultrcold atom experiments, people usually use time-of-flight technique to measure the momentum distribution, then get the condensate fraction information from the interference pattern. What is the ...
2
votes
1answer
78 views

How does temperature affect an electrical current

Synopsis I have read an interesting article J. Halderman et al. "Lest we remember: cold boot attacks on encryption keys" in computer science regarding cold booting. The paper discusses how the use ...
5
votes
2answers
274 views

Naive questions on Goldstone modes and a possible duality relation?

For example, let's consider a 1D spin-1/2 ferromagnetic (FM) Heisenberg chain $H=-J\sum_{i=1}^{N}\mathbf{S}_i\cdot\mathbf{S}_{i+1}$ with periodic boundary conditions. Now we want to study its low ...
2
votes
1answer
69 views

Hamiltonian for the Periodic Kitaev Model

The Hamiltonian for a system of spinless fermions on a 1D chain (with chemical potential $\mu=0$) is given by $$ H=-\sum_j\left( c^\dagger_{j+1} c_j+h.c.\right)+\Delta \sum_j \left( ...
0
votes
0answers
90 views

Gutzwiller mean-field method in Bose Hubbard model

Gutzwiller mean-felid method is an efficient way to study Bose-Hubabrd model in optical lattice with a harmonic trap. Gutzwiller method assumes there is no spatial correlation within the trap, so ...
3
votes
1answer
175 views

Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, ...
0
votes
0answers
58 views

Question about Bose-Hubbard Model

By using an optical lattice, how can one change the interaction term $U$? And how is the superfluid phase achieved in the hard-core boson regime? Why are these phases identified as superfluid or mott ...
1
vote
2answers
239 views

Why are Cooper pairs formed by electrons of opposite momentum and spin?

I understand that Cooper pair in low-temperature superconductivity are formed by electron-phonon interaction. Normally one then assumes that electrons of opposite momentum and spin are paired. This is ...
1
vote
0answers
57 views

Should Brillouin zone be a continuous object rather than a discrete one in the thermodynamic limit?

For example, just consider a 1D atom chain with $N$ sites and lattice constant $a=2\pi$, under periodic boundary conditions, the crystal momentum reads as $k=\frac{n}{N}\frac{2\pi}{a}=\frac{n}{N}$, ...
2
votes
1answer
51 views

How does band gap vary with the cell volume?

How does band gap vary with the cell volume? is there a relation? If the volume is compressed, the interaction between atoms would be more, therefore the perturbation is higher hence the splitting ...
2
votes
1answer
111 views

Why do He-3 atoms repel each other much more strongly than electrons?

Is there a simple answer to this question ? see last line of this paragraph http://en.wikipedia.org/wiki/Fermionic_condensate#Fermionic_superfluids
0
votes
0answers
74 views

Questions on degenerate ground states and the thermodynamic limit?

For example, let's consider a $N$ spin-1/2 system on a lattice described by the Hamiltonian $H$. My questions are: (1) If $H$ has either global $SU(2)$ spin-rotation symmetry or time-reversal ...
5
votes
1answer
155 views

Will all physical quantities unchanged by this transformation?

I am reading an article about Bloch-Floquet state. My questions is in Part II.B and Appendix A of this paper, I will describe them below. The original Schordinger equation we consider is: ...
5
votes
1answer
224 views

Degenerate perturbation theory applied to topological degeneracy?

Consider a quantum system described by a gapped Hamiltonian $H_0$ with degenerate ground states (GS), adding a perturbation term $V$ to $H_0$, then the low-energy physics can be described by an ...
3
votes
1answer
199 views

Naive questions on the ground states of Kitaev model

I got some naive questions on the ground states of honeycomb Kitaev model (with open boundary conditions): (1) Consider a simple case that $J_x=J_y=0$, then the model reduces to $$H=J_z\sum_{z\text{ ...
3
votes
1answer
81 views

Help with 1D and 2D density of states

I am currently looking at changes in DOS when sampling recipocal space finely. More precisely, I am looking at the expressions $$\rho_\text{1D}(E)\text{d}E = \frac{m}{\pi \hbar} \sum_i ...
0
votes
0answers
48 views

band gaps in tight binding model

What happens at the zone boundaries of the brillouin zones in the tight binding model? How does the band gap originate in the TB model?
4
votes
3answers
184 views

Proving a step in this field-theoretic derivation of the Bogoliubov de Gennes (BdG) equations

In derivation of the BdG mean field Hamiltonian as follows, I have a confusion here in the second step: $H_{MF-eff} = \int ...
0
votes
0answers
46 views

A small contradiction between periodic boundary condition and first Brilliouin zone

In condensed matter, one usually considers Bloch states inside the first Brilliouin zone, which, for 1d system with lattice constant $a$, is $-\pi/a<k<\pi/a$. But the basis of this, Bloch ...
1
vote
0answers
76 views

Variational principle

In the LMTO method, the interstitial region is approximated by plane waves and the muffin tin region of the potential by solutions to the radial Schrodinger equation. In using the variational method ...
1
vote
1answer
133 views

Significance of magnetic translation operator defined in fractional QHE's description

What is the significance of the magnetic translation operator used in describing the Fractional Quantum hall effect? I was following Anthony Leggett's lecture video in which he defines these operators ...
3
votes
0answers
199 views

Is non-relativistic quantum field theory equivalent with quantum mechanics?

Related post Can we "trivialize" the equivalence between canonical quantization of fields and second quantization of particles? Some books of many-body physics, e.g. A.L.Fetter and ...
3
votes
0answers
492 views

Numerical problem in solving the Bogoliubov de Gennes equations- methods to solve?

I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} ...
3
votes
1answer
171 views

confusion in discrete transform to solve kronig penney matrix equation in fourier space

I have a periodic potential $$V(x) =\sum_{K}e^{iKx}V_{K} =\sum_{n}e^{\iota2\pi nx/a}V_{n} $$ where $K =\frac{2\pi n}a$ is the reciprocal lattice vector and $a$ is the lattice constant and $n =\pm ...
2
votes
0answers
90 views

physical intuition behind quasi-bound state formation in feshbach resonance

In Feshbach resonance, by scattering theory formalism it is found that the resonance in cross-section happens when bound state energy of the closed channel is near to the scattering state energy of ...
3
votes
0answers
42 views

how is feshbach resonance potential term physically produced?

In Feshbach resonance model, a 2*2 potential term with space dependent diagonal and non-diagonal terms is written $\left(\begin{array}{cc} V_{11}(\mathbf{r}) & V_{12}(\mathbf{r})\\ ...
3
votes
2answers
142 views

How to derive the Aharanov-Bohm effect result?

In the derivations of the Aharonov-Bohm phase, it is directly mentioned that due to the introduction of the vector potential $A$, an extra phase is introduced into the wavefunction for case $A\neq0$ ...
1
vote
2answers
590 views

Dispersion Relation (e vs. k) clarification (crystal momentum or electron momentum)

If we get the dispersion relation from the Fourier transform of the lattice vectors then how do we get electrons information? Specifically, for the $k=0$ point of the graph, does this mean the ...
0
votes
0answers
27 views

Theorem of inclusion in the disordered Bose-Hubbard model

In a paper by V. Gurarie et al. , the theorem of inclusion is used to prove that there is no direct phase transition between Mott insulator and spuerfluid in presence of disorder. In Fig. 2 of that ...
1
vote
0answers
38 views

spread of fock state distribution and infinite revival time of rabi oscillation in spontaneous emission

In cavity QED for a 2-level atom, the revival time for oscillation b/w the states $\left|\ e\ 0\right\rangle$ and $\left|\ g\ 1\right\rangle$ (absorbing the same photon that is emitted) is said to be ...
2
votes
2answers
179 views

A conceptual question about Green's function's treatment of interaction

Here we have electron gas and some other stuff. We expand the Hamiltonian to the 1st order of one single harmonic oscillator's displacement $\vec{u}$. Its equilibrium position is at the origin. Then ...
0
votes
2answers
77 views

Is crystal momentum an operator?

My teacher has for Bloch waves the notation $\langle \vec{r}|\vec{k} \rangle = e^{i\vec{k}\cdot \vec{r}}u_{\vec{k}}(r)$ and uses it consistently. However, does this not assume that there is an ...
4
votes
0answers
152 views

Finding the ground state of the toric code Hamiltonian

How do I write by proof, the ground state of the toric code (by Kitaev) Hamiltonian $ H=-\sum_{v}A(v)-\sum_{p}B(p) $ where $A(v)=\sigma_{v,1}^{x}\sigma_{v,2}^{x}\sigma_{v,3}^{x}\sigma_{v,4}^{x}$ and ...
0
votes
0answers
26 views

Is there a generic term for orbital groups such as $e_g$ and $t_{2g}$?

I am looking for a generic term for sets of atomic orbitals (viz. spherical harmonics) which are grouped by crystal symmetry. The most familiar examples would be $e_g$ and $t_{2g}$ (in cubic ...
1
vote
0answers
160 views

How do I write the Hamiltonian for a 3-level system?

I came across following types of three-level systems like V-system, Λ-system and 2-photon absorption It seems that their Hamiltonians can be written intuitively by checking out the coupled levels ...
3
votes
1answer
118 views

Do holes have wavefunctions?

Do holes (as in the absence of an electron) have wavefunctions? In my understanding, when we talk about holes, we are implicitly invoking two multiparticle wavefunctions: $$\tag{1} \Psi(x_1,...,x_N)= ...
3
votes
1answer
131 views

Group analysis forbids band-crossing in 1D?

Group analysis forbids band-crossing in 1D in terms of conventional band theory. I read this in a good solid state physics book. But there's no explanation at all. Can anyone help on this?
1
vote
1answer
104 views

Coupling of open and closed channels in Feshbach resonance model

Feshbach resonance is described with coupling of 2 systems differing in the form of potentials :- one is said to produce a bound state (in 'closed' channel) and other is to produce scattering states ...
4
votes
3answers
134 views

Why can we quantize macro(meso)scopic harmonic oscillator?

It is well known that we have got many kinds of quantized macro(meso)scopic harmonic oscillators or so in tiny mechanical systems. People are talking about cavity cooling and so on. However, it is ...