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A capacitance bridge setup is good. One branch contains the known variable capacitance and a resistor. The other arm a resistor and the ferroelectric material. Adjust the known for null output.

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A simple way to do this requires an LCR (inductance, capacitance, resistance) meter, an oven/furnace/hotplate, and a thermocouple. With an LCR meter, you can measure the capacitance as well as the loss tangent, $\delta$ at the same time. If you attach a thermocouple to the sample, and ramp the temperature slowly (less than 1 Celcius/min), you can measure ...

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You question is a bit unclear. The red region of the P-E diagram that you show comes from the equation for Gibbs free energy in a ferroelectric, with the electrostatic term: $G= \frac{1}{2} \alpha_{1} D^{2} +\frac{1}{4} \alpha_{2} D^{4} +\frac{1}{6} \alpha_{3} D^{6}-E*D$ Taking the derivative with respect to D: $\frac{ \partial G}{ \partial ... 3 You can think of Hartree-Fock as a self-consistent mean field method. The idea is that you start with each of the particles in their initial orbits. These particles generate a mean field, and you can solve for single-particle eigenfunctions of this mean field. This is done by solving the time-independent Schrodinger equation $$... -1 try to use LTM method to measure ohmic contact between metal and semiconductor? 1 The correlation function measures, as you would expect, how correlated two random variables are. That is, how often two random variables have similar values. We can construct such a function very simply. Say you are flipping coins, and you want to know if their results are correlated. To quantify things, call "heads" +1 and "tails" -1. To make ... 0 To obtain the energy gap in the thermodynamic limit, one should take N\rightarrow\infty, V\rightarrow\infty where N is the number of atoms and V the system size, but hold N/V (i.e. density) fixed. In your case, it means simply taking N to \infty is enough and keep all t, u, \alpha fixed for now. This tight-binding model can be solved exactly. ... 2 Intuitive answer: Keep in mind that in three dimensions you can have point (no dimension) and line (1D) defects. If you mean line defects, you're right, 2\pi line defects are unstable (although 2\pi point defects are stable). In a 2D nematic, only point defects are possible and you're also right: a 2\pi disclination in a 2D nematic is stable (in the ... 0 A zero-field-cooled/field-cooled split in the magnetic susceptibility vs. temperature doesn't have to be superparamagnetism. In the case of superconductors, if we apply a field to the material and cool past T_c, some flux can be trapped inside, but if we cool first and then apply field, that flux will be shielded away, resulting in greater diamagnetism. 0 As I expected, this simple question calls for no more than a little sleight of hand, as pointed out by the sole comment above. It looks as if @Meng Cheng won't make it an answer. Thanks to him. And here I confirm that it works well. 1 The poster above is incorrect: FCC metals do not have a ductile to brittle transition temperature and instead remain ductile at low temperatures. This is because the stress required to move dislocations is not strongly temperature-dependent in FCC metals, and thus failure occurs by plastic flow instead of crack propagation. In BCC metals, the stress ... 0 It is posslible to do this proof in a direct way using a slightly different and in my opinion a lot more sensible approach to the creation/annihilation operators. I will write it up here for the benefit of any interested. The inner product of N particle states can be written as:$$ \langle\chi_1,...,\chi_N|\Psi_1,...,\Psi_N\rangle= \det ... 0 Because $$n_\downarrow n_\downarrow = n_\downarrow$$ and similarly for$n_\uparrow$. Why? Because$n_\downarrow$can only take on the values 0 or 1 and $$0^2=0$$ and $$1^2=1$$ 3 The ground state of the toric code can be understand as a superposition of all loop configurations in the$z$basis. The fact that these loops fluctuate at all length scales (and thus around the torus) leads to the topological order in the system. The$\sigma_z$terms lead to a "tension" in the loops, penalizing long loops. Eventually, this tension will ... 1 In the modern crystallography there is a notation of aperiodic crystals (or quasicrystals). They are crystals with normal basis$\mathbf a,\mathbf b,\mathbf c$and a set of propagation (or wave)$\mathbf k$-vectors that are incommensurate with the metric$\mathbf a,\mathbf b,\mathbf c$. The atomic positions (or/and occupancies) are modulated according to ... 0 This is pretty straight forward. All you need to do is measure the capacitance of the sample at constant frequency and at different temperatures. Imagine the sample as a parallel plate capacitor of thickness D and area A. Now Dielectric constant E = C D/A. With these calues you can plot the values w.r.t different temperatures and arrive at your curie ... 0 In addition to what Meng Cheng said, remark that the mean-field Bogoliubov-Gennes Hamiltonian, say $$H=\sum_{k}\left(c_{k}^{\dagger}H_{0}c_{k}+\Delta_{k}c_{k}c_{-k}+\Delta_{k}^{\ast}c_{-k}^{\dagger}c_{k}^{\dagger}\right)$$ can be diagonalised by the Bogoliubov transformation you mentioned : ... 0 You need to perform tensor product of the matrices. By doing this you will get the matrix with the dimension 4x2=8. The similar tensor product you should perform with the wavefunctions, so they span 8 dimensional space. Your new wavefunction will be a vector in this new basis. 1 For each value of$k$, the above hamiltonian has energy contributions for an electron hopping from an$A$to a$B$site and vice versa. If we wanted to write the hamiltonian in matrix form (in a basis corresponding to$A$and$B$sites), it would look like H_0 = \sum_{k,\alpha}\left(\begin{array}{c c}0& J_0\gamma_{k,\alpha}\\ ... 0 Electrons in the insulator are tightly bound to the ions.The extra electron on an insulator cannot move as conduction band is completely empty for an insulator. So technically the electron will be localized wherever its placed on an insulator.As it does not belong to or correspond to any specific atom, you cannot assign quantum numbers to that ... 0 The wetting behavior is basically defined through the surface and interface energies. A material A will wet material B if: $$E_{surf}(A) + E_{int}(AB) < E_{surf}(B)$$ The surface of material B is minimized by wetting material A (and therefore leading to layer-by-layer growth. The reverse case leads to island formation, namely if: $$E_{surf}(B) + ... 0 The localization of Majorana zero modes has a well-defined meaning: consider a Kitaev chain with two ends. Because of the zero modes, there are two nearly degenerate ground states, let us call them |0\rangle and |1\rangle, which have opposite fermion parities. They are localized as "single-particle wavefunctions" in the following sense: if one computes ... 1 The zeroth order term is M=g\mu_B/2. To get the leading correction, you can substitute this on the r.h.s. of your last equation, which gives$$ M = \tfrac{g\mu_B}{2}(1-2\exp[-\tfrac{2T_c}{T}M])\ . $$(This is justified since the effect of any small correction in the exponential will be extremely small for small T.) Note that Bloch's law is derived by ... 1 Hint: a_3^\dagger a_3 commutes with H, so your states can be simultaneous eigenstates of both operators. Then you are left with a linear Hamiltonian that you can diagonalize. 4 The mean free path can be meaningful quantity in quantum mechanics, although usually only in a semi-classical regime. It is particularly useful in the kinetic theory of quantum liquids at low temperature, where the excitations of the system can be described as quasiparticles that propagate approximately ballistically and interact only rarely. You can define ... 2 For one thing, toric codes (and other error-correcting codes) are really about ways to store quantum information(logical qubits) in several physical qubits, so there is not much point in asking for a continuous limit. On the other hand, if you view it as a topological quantum phase of matter, then surely there are continuous versions. For example, the ... 3 The gap of the parent Hamiltonian does not depend on the number D of blocks (at least not directly). The spectral gap of the parent Hamiltonian in the block-injective case is analyzed and a lower bound is given in B. Nachtergaele, Commun. Math. Phys. 175, 565 (1996), arXiv:cond-mat/9410110. 0 It belongs to the symmetry class of no symmetry. i.e. the only symmetry is the fermion-number-parity conservation Z_2^f, which is always the symmetry of fermionic systems. See my paper http://arxiv.org/abs/1111.6341 for a discussion on the full-symmetry group G_f for fermion systems. 3 You are in luck. Alexander Gavriliuk, Ivan Trojan, and Viktor Struzhkin observed the anticipated transition in 2012. Their paper is in Physical Review Letters 109 086402 (2012) (link to the paper). They mention Mott's prediction in the abstract, and discuss the various prediction of where it would occur in comparison to what they observed. Now, they had ... 1 Measuring an off-axis peak simply means that you're looking for crystal planes, which are not parallel to the sample surface. Therefore, they have an in-plane component (in addition to the perpendicular lattice plane spacing, which is commonly measured), which is the part, you're looking for. 1 In some sense, you have answered your own question. All this means is that you cannot determine a from a series of reflections along the same axis (e.g. (001), (002), (003), etc.). These are all along that same direction in reciprocal space, so therefore they are all on the same axis. If you measure an off-axis reflection, you will able to calculate ... 1 Both ways are equally valid and yield identical answers. If you wanted to convince yourself, get the single complex \psi equation, write \psi = |\psi|e^{i\phi}, and you'll find that you've reproduced the |\psi|, \phi equations of motion. Varying w.r.t. \psi or the real components are the same because of the product rule applied to \psi: ... 2 The two are confusingly similar. Heat transfer coefficient is given by:$$ h = \frac{q}{\Delta T} $$where q is heat flux. This corresponds to the ratio of heat flux to the temperature difference between two points. Thermal conductivity is often given by:$$ k = -\left|\frac{\mathbf{q}}{\nabla T}\right| $$i.e. the ratio between the heat flux vector, and ... 1 They have been observed in the following experiment: arxiv.org/abs/1310.7563 In this paper, there is a periodic laser pulse hitting the sample which gives a time-periodic Hamiltonian. They then used ARPES (angle-resolved photoemission) to see the band structure repeated in energy steps, \epsilon_n=\hbar \omega_n. Without the time-dependent laser pulse, ... 0 The classical Ising model$$ H=\sum_i \sigma^z_i\sigma^z_{i+1}$$has two degenerate ground states with a constant gap above (2 for periodic boundary conditions). This can be easily generalized to models with more than 2 states and correspondingly higher ground space degeneracy (Potts models). 0 In the XXZ spin chain, there exists some regime where the ground state becomes doubly degenerated in the infinite volume limit. This degeneracy produces a gap in energy between the ground state and the first excited state. As far as I know, on the finite chain, there is no degeneracy at all : the gap is therefore not independent of$n$. I don't know if such ... 1 The brief answer is yes, they do have topological degeneracy. My understanding is that if you only focus on the surface topological order with some symmetry given by the bulk symmetry protected topological (SPT) state, there is nothing wrong with that symmetry enriched topological order (SET) states. That means they also have all the properties as the usual ... 0 for each defect level, the energy value was not constant. If atom configuration relaxed, value would change into parabolic curve. As mentioned by upper user, ZPL was the difference between the lowest values of excited state and ground state. And ZPL line have a distinct peak in experimental spectrum. 0 Your idea is correct: at low temperatures, "dirty" or doped semiconductors conduct better than clean ones. In fact, doping has been very seriously studied not just to tune the conductivity of semiconductors but to obtain spatial control of conductivity by doping profiles, so you can really pattern a circuit made of doped silicon in silicon. The way it works ... 2 The density of states$\rho(E) \propto E^{1/2}$is valid only for free electrons. Electrons in a solid are certainly not free, and the density of states is complicated. Certainly: the density of states is zero inside the band gap. 3 In the Ising anyon model, there are three topological charges,$1,\sigma,\psi$.$\sigma$can be thought as carrying a Majorana zero mode, and$\psi$is an ordinary fermionic excitation. This can also be understood in the context of$p_x+ip_y$superconductor, where$\sigma$is the non-Abelian vortex and$\psi$is the Bogoliubov quasiparticle. Braiding$\psi\$ ...

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