Transitionless quantum driving for specific eigenstates
Transitionless quantum driving is a concept that was invented by Berry in 2009. In his article on transitionless quantum driving he showed that it is possible to speed up adiabatic evolution of...
View ArticleIn an adiabatic process, if there is no heat flow between system and...
How can the temperature of a body change unless heat flows in or out of it?So shouldn't all adiabatic process be considered isothermal too? but that is not true as both the processes have different...
View ArticleChange in temperature due to adiabatic expansion against the vacuum
Let's consider an ideal gas that expands in vacuum and it is thermally isolated from the surroundings. Since it is isolated, it does not exchange heat with the exterior $Q=0$. Since it is expanding...
View ArticleTemperature increase in fixed volume due to gas injection
I have a vessel of fixed volume with adiabatic boundary which is initially filled with air at pressure of 1 atm and temperature of 300 K. Now, I inject air from an external source at a fixed flow rate...
View ArticleWhy do we need an adiabatic expansion in the Carnot cycle? [duplicate]
As we know that 1st process is an reversible isothermal expansion during this the system is in quasi static equilibrium which helps in increasing the volume of the system but why does the second step...
View ArticleBerry phase disappearing in adiabatic approximation?
The celebrated adiabatic theorem states that for a system initially in the eigenstate $|\psi(0)\rangle = |n(0)\rangle$ for $t=0$, it will stay in that state afterward under adiabatic...
View ArticleWhy is an adiabat steeper than an isotherm in a $p$-$V$ curve?
What I have so far gathered is a mathematical explanation.Since for an adiabatic process, $pV^γ=$ constant, for a unit change in pressure, change in volume would be very less. Therefore, if compared to...
View ArticleAdiabatic process and internal energy
My question concerns the connection between change in internal energy $dE = Q - W$ and the available work in an adiabatic process.My understanding is, that in an adiabatic process ($Q=0$) the change in...
View ArticleDry adiabatic lapse rate
Adiabatic lapse rate is defined as$$\Gamma_a \equiv -\left(\frac{dT}{dz}\right)_{\rm parcel}=-\frac{R_{\rm a} T}{c_p \,p}\left(\frac{dp}{dz}\right)_{\rm parcel} = \frac{g}{c_p}$$$R_a$ is gas consntant...
View ArticleAdiabatic piston: why is Callen's argument flawed?
This question is related to this one. I would ask you to read that question and my answer to the question itself before answering this one.The problem is the following. In his book Thermodynamics,...
View ArticleFinding condition for Adiabaticity
I have a differential equation describing a resonator that looks like this:$$ \frac{d\alpha(t)}{dt} = [j a - b]\alpha(t) + \sqrt b e^{jct}$$ where I can solve it putting: $$\alpha(t) = \alpha...
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Isothermal and adiabatic compression in the Carnot cycle
I am reading about the Carnot Engine and I understood the first 2 stages (Isothermal and Adiabatic Expansion) well. In the 3rd stage where isothermal compression takes place, the surroundings do work...
View ArticleAdiabatic closed system work
The closed system work PdV is path dependent but it is path independent for an adiabatic process as can be shown by applying conservation of energy on a closed system (dQ = dE + PdV),here dE is change...
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How does the state variables $(P,V)$ remain constant for a system with...
I have been very confused regarding how my physics textbook differentiates b/w an adiabatic wall and a diathermic wall.The term ‘equilibrium’ in thermodynamics appears in a different context: we say...
View ArticleRabi oscillations within the adiabatic theorem?
I'm studying Rabi oscillations in a two-level system (TLS) with Hamiltonian\begin{align}H(t)=\omega_0 \sigma_z + \Omega \cos(\omega_1 t) \sigma_x.\end{align}The model is usually treated within the...
View ArticleWhat is the relation between the Adiabatic Approximation used in quantum...
I am an aspiring quantum chemist and have come across two vastly different versions of the Adiabatic Approximation when studying Quantum Mechanics from the perspective of physics and chemistry...
View ArticleThe contradiction between Gell-mann Low theorem and the identity of Møller...
This question originates from reading the proof of Gell-mann Low thoerem.$H=H_0+H_I$, let $|\psi_0\rangle$ be an eigenstate of $H_0$ with eigenvalue $E_0$, and consider the state vector defined...
View ArticleDerivative of $c(t)$ in Adiabatic Approximation
In Sakurai's Modern Quantum Mechanics, second edition, $5.6.10$ is$$\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\right]...
View ArticleNon-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...
View ArticleAdiabatic theorem for a 3-level system
If I have a 2-level system, with the energy splitting between the 2 levels $\omega_{12}$ and an external perturbation characterized by a frequency $\omega_P$, if $\omega_{12}\gg\omega_P$ I can use the...
View ArticleBit structure in Adiabatic Quantum Computing [closed]
https://arxiv.org/pdf/quant-ph/0007071.pdfIn 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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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...
View ArticleAdiabatic volume change of an ideal gas thought process
I am struggling with trying to solve the following problem, attempting just (a) and the first part of (b) for this exercise:During a reversible adiabatic volume change of an ideal gas, $PV^{\gamma}$...
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Adiabatic Availability?
In the textbook "Thermodynamics: Foundations and Applications" by Elias P. Gyftopoulas and Gian Paolo Beretta (Dover). In chapter 5, on page 73 (section 5.3) the book says: Adiabatic availability is...
View ArticleWhy 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...
View ArticleGiven state $P$, does the set of all forward adiabatic processes and reversed...
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...
View ArticleConstructing 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 $$H_0 = H + 2\sigma^x_{i_0} \qquad H_1 = H + 2\sigma^x_{i_1}$$...
View ArticleCalculation of adiabatic flame temperature [closed]
It's given Pulverized coke is combusted through a burner along with preheated air. The concentration of coke powder in the coke-air mixture is 360 gm/Nm3, and the fuel-air mixture is supplied at the...
View ArticleWhen applying the adiabatic theorem, why doesn't the gap become doubly...
Suppose we have a parameterised family of Hamiltonians $H(s)$, $s\in [0,1]$, acting on $n$ spins/qubits. When applying the adiabatic theorem, it is well known that if we wish to remain in the ground...
View ArticleWork done in adiabatic process irreversible and reversible
Work done for adiabatic reversible process is $$(P_1V_1 - P_2V_2)/(γ-1)$$ but this is also the work done for adiabatic irreversible process. How?
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