Questions tagged [adiabatic]
Thermodynamic processes that occur without exchanging heat between the system and its environment.
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Thermodynamics exercise on transformations
An exercise in my book states the following:
n = 0.42 moles of an ideal biatomic gas are stored in an adiabatic cylinder with volume $V = 10^{-2} \text{ m}^3$, with an initial pressure equal to one ...
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Adiabatic Approximation in the spin 1/2 System
I am studying the following Hamiltonian:
$$H(t) = \begin{bmatrix}
\frac{t\alpha}{2} & H_{12} \\
H_{12}^* & -\frac{t\alpha}{2} \\
\end{bmatrix}$$
I want to assume that $\...
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Is the increase in the internal energy of an ideal gas equivalent to an increase in thermal energy?
ΔU = Q - W
Q: Heat received by the gas from the surroundings (positive if received, negative if given to the surroundings)
W: Work done by the gas on the surroundings (positive if done on the ...
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Finite-time effects in Landau Zener
Consider a two level system with a Landau-Zener Hamiltonian of the form
$$\hat{H}=\begin{pmatrix}v t&\beta\\\beta&-v t\end{pmatrix}.$$
The Landau-Zener formula provides a closed form for the ...
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Entropy in irreversible adiabtic process
We know that,
$$dS=\dfrac{\delta Q_{rev}}{T}$$
If you have an irreversible adiabatic process between two thermodynamic equilibrium end states of a system, there exists no possible reversible adiabatic ...
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Adiabtic aproximation and MSW effect
I have been reading about the MSW effect in neutrinos from supernovae. In some papers, it's assumed the "adiabatic case" which, according to the book "Neutrino Physics and Astrophysics&...
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Origin of ideal gas fluid dynamics equations including the adiabatic index
I was given a system of equations that supposedly describes the fluid dynamics of an ideal gas.
The equations are:
$$
\begin{align}
&\frac{\rho}{m} = \frac{p}{T} &\text{(ideal gas law)} \\\\
&...
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Modelling the number of times a gas tank can be filled
I'm currently working on a project where I need to estimate how many times a large, high-pressure gas tank can refill a smaller tank. For this purpose, I'm using a pressure regulator to manage the ...
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Constructing a gapped family of Hamiltonians in the trivial paramagnet
Consider the trivial paramagnet, which has the Hamiltonian $$H = - \sum_i \sigma^x_i$$ Now let's say I have two different Hamiltonians $$H_0 = H + 2\sigma^x_{i_0} \qquad H_1 = H + 2\sigma^x_{i_1}$$ ...
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Given state $P$, does the set of all forward adiabatic processes and reversed adiabatic processes reach all states in the state space?
Let $A$ be a thermodynamic system and let $\Sigma$ be its state space. By the state postulate, if $A$ has $n$ two-way work channels (i.e. ways in which work can be done both positively and negatively ...
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Why doesn't $\gamma = \frac{5}{3}$ for all adiabatic processes
For monoatomic, ideal gases, $PV^{\frac{5}{3}}$ is constant. I have been told that this does not hold for diatomic, or other non-monoatomic gases. However, I derived the relationship using only the ...
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Why slow compression with conducting walls should be isothermal?
I know that for an isothermal process heat transfer is necessary so process should be slow and walls should be conducting for heat transfer to occur as a process cannot be isothermal and adiabatic at ...
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Bit structure in Adiabatic Quantum Computing [closed]
https://arxiv.org/pdf/quant-ph/0007071.pdf
In Chapter 6 in the paper "A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability”, by Edward Farhi, Jeffrey ...
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Non-adiabatic evolution and time-dependent adiabatic parameter
I am dealing with the dynamics of a two-bands lattice system. The idea is that you have a lattice model of free fermions, with some hopping amplitudes and on-site energies.The lattice have two fermion ...
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Derivative of $c(t)$ in Adiabatic Approximation
In Sakurai's Modern Quantum Mechanics, second edition, $5.6.10$ is
$$\begin{aligned}
\dot{c}_m(t)=-\sum_nc_n(t)e^{i[\theta_n(t)-\theta_m(t)]}\langle m;t|\left[\frac\partial{\partial t}|n;t\rangle\...
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