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Questions tagged [adiabatic]

Thermodynamic processes that occur without exchanging heat between the system and its environment.

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Basic Thermodynamics: Quasistatic Adiabatic Process

I'm going through the exercises in a Thermodynamics book, just to revise and build my intuition. Right now, I'm working on: Show that for a quasistatic adiabatic process in a perfect gas, with ...
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1answer
173 views

How does adiabatic cooling make a nebula colder than the CMB?

According to measurements, the gas from the Boomerang Nebula is expanding so fast that it's colder than the cosmic microwave background radiation... how does such a simple mechanic work on such a ...
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958 views

Adiabatic invariant and Liouville's theorem

It appears that many people have tried to show adiabatic theorem from Liouville's theorem, e.g., Li's note, or at least tried to find some relations, e.g., Rugh, Adib and Tong's lecture notes Sec. 4.6....
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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 ...
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145 views

Where is wrong in the derivation about adiabatic theorem

There is a homework in Quantum Mechanics which is about adiabatic theorem. Let us argue where is wrong in following derivation. $$i \partial_t |\psi(t)\rangle = H(t) |\psi (t)\rangle \tag{1}$$ if $\...
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Importance of energy relation in Landau & Lifschitz “Statistical Physics”?

At the end of section 11 in "Statistical Physics" by Landau & Lifschitz, a supposedly important equation is derived. ... Comparing (11.1) with (11.2) we find: $$\frac{\overline{\partial ...
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229 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 ...
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118 views

Different forms of the Adiabatic Theorem

I've been reading several papers on Adiabatic Quantum Computation, and I am confused by the form in which the adiabatic approximation condition is presented. For example (quant-ph/0001106 eq 2.8) \...
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4answers
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Thermodynamic process

"During this process, the system is always in thermal equilibrium with the surroundings." Does this statement means the process is adiabatic? Since the temperature of both systems is the same, there ...
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102 views

Energy Level Change in Adiabatic Reversible Process

I am currently trying to get my head around the concept of entropy. One way to understand it is that it can be related to the number of available energy levels in a system. From what I read, the ...
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316 views

Adiabatic fluctuations

In Baumann's cosmology lecture,http://www.damtp.cam.ac.uk/user/db275/Cosmology/Chapter4.pdf , chapter 4, page 89, he defines adiabatic perturbation as: Adiabatic perturbations have the property ...
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3answers
484 views

Thermal expansion of solid body and calculation of work produced

From the information about thermal expansion on Wikipedia, I found that if I heat a steel rod that's 1-meter in length and 1-cm in diameter steel rod to 100 degrees Celsius, then it will expand by ...
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148 views

Phase-shifting of instantaneous eigenstates in the adiabatic approximation

In my book Quantum Mechanics by B.H. Bransden and C.J. Joachain, there is a chapter on the adiabatic approximation. Here, the authors assume that the time-dependent Hamiltonian $\hat{H}(t)$ changes ...
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1answer
409 views

Plotting isothermals and adiabats

first time poster in this site. I am trying to create a small program to make a graph of the Carnot cycle. For isothermals I am simply trying to look for points where P*V would give the same ...
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180 views

Ordering of eigenstates in the quantum adiabatic theorem

Suppose we have an 'initial' Hamiltonian $H_{i}$ whose eigenvalues are all non-degenerate, which we order as follows: $ E^{0}_{i} < E^{1}_{i} < \dots < E^{N-2}_{i} < E^{N-1}_{i}$ Suppose ...
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Adiabatic approximation and time-dependent problems

I am an undergraduate physics student. I have a question in approximation methods for time-dependent problems in quantum mechanics. I read the proof of the adiabatic theorem but I didn't understand it....
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83 views

Adiabatic evolution for initial Hamiltonian on Hadamard basis and problem Hamiltonian as diagonal

This is spawned from a comment at the answer to one of my previous questions. Someone suggested to me that claiming the following statement might be NP-hard. Could anyone please help me to figure out ...
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162 views

Adiabatic theorem in the regime of quantum optics

I am wondering whether there is a version of adiabatic theorem in the regime of quantum optics. My understanding of quantum optics involves with the interaction between photon and atom. This ...
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647 views

Infinite quantum well width $L$ to $2L$ adiabatic process

If we change width of the infinite quantum well $L$ to $2L$ slowly enough, how it does change energy levels.
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35 views

Adiabata for Van der Waals equation

Adiabata for ideal gas has equation $pV^\gamma = const.$ this allows calculate $p(V) = K/V^\gamma$, where K is some constant. Is there similar equation and preferably function $p(V)$ for gas ...
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2answers
52 views

Why does an adiabatic process become an isothermal process when D.O.F. are high?

Say that during an adiabatic process, the pressure changes from $p_0$ to $a*p_0$, and let the heat capacities ratio be denoted by b ; using the basic adiabatic relations for an ideal gas, we can find ...
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34 views

What is the difference between arriving at the 'avoided crossing' point of a two level system adiabatically and non-adiabatically?

In the simplest case of the 'avoided crossing phenomenon' we can assume a two level system that its eigenstates $E_1(n)$ and $E_2(n)$ are functions of some continuous variable n, and there is some ...
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36 views

Deduce if path is adiabatic from the state space

Can we deduce, for quasistatic processes, if a process is adiabatic by purely looking at its path in state space? Take, for example, the process of stirring a liquid to heat it up (adiabatic) and ...
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1answer
520 views

Adiabatic 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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252 views

Can steam freeze via adiabatic expansion?

Context: At the end of animation movie Steamboy, a huge steam engine's pressure vessel breaks, which results in the escaped steam freezing to ice. I've been thinking about this -- is it really ...
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66 views

Question about adiabatic process (in Landau&Lifshitz's book)

In section 11 of Landau's statistical physics part 1, he wrote the following: Let us suppose that a body is thermally isolated, and is subject to external conditions which vary sufficiently slowly. ...
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3answers
456 views

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 ...
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3answers
164 views

Is it possible to increase the temperature of an ideal gas in an adiabatic sealed container with a frictionless piston for a lid?

As far as I understand it, if I pumped the piston repeatedly, compressing the gas, the temperature would go up for a second, but the minute I released the piston the higher pressure inside the ...
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150 views

Is the adiabatic theorem in Quantum mechanics valid in general for Non-Hermitian Hamiltonians?

Is the adiabatic theorem in Quantum mechanics valid in general for Non-Hermitian Hamiltonians? The proofs I have come across for adiabatic theorem all assume at some point in the proof that the ...
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2answers
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Derivation of $(\partial S/\partial X)_{E}+(\partial S/\partial E)_{X}f=0$ in Chandler's Statistical mechanics book

I am having trouble understanding something very introductory in Chandler's statistical mechanics book regarding the derivation of $(\partial S/\partial X)_{E}+(\partial S/\partial E)_{X}f=0$ The ...
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Slowly Varying Functions for Adiabatic Invariants - The Same as Karamata's?

In section 49 (and 50) of Landau and Lifschitz's "Classical Mechanics", adiabatic invariants are discussed, which are related to functions which vary adiabatically or "slowly" with time. Admittedly ...
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Are there any specific examples of the application of Lewis-Riesenfeld procedure to time dependent Hamiltonians in QM?

Lewis-Riesenfeld invariant theory is a theory applicable to solve time-dependent Schrodinger equations. I have always encountered the theory related to the procedure, however never encountered any ...
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1answer
492 views

Dry 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 ...
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1k views

Calculating mass flow rate, force of thrust produced compressed air discharge

This one's a bit of a doozy, so please feel free to comment on any one single part or parts to this physics problem. The setup is simple--I have a container (an empty bottle) which I fill with a ...
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206 views

Why doesn't entropy get decreased in adiabatic expansion process?

I was reading the second step of Carnot cycle in which the system undergoes adiabatic expansion doing work & thus decreasing the internal energy of itself. The entropy didn't change as no further ...
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244 views

Adiabatic Surfaces in thermodynamics

In some lecture notes on thermodynamics there is a discussion as to whether by assuming the first law of thermodynamics alone we can prove the existence of a adiabatic surface in three dimensions. To ...
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216 views

Temperature change in adiabatic free expansion

Consider a gas with fixed number of particles $N$ undergoing adiabatic free expansion from $V_1$ to $V_2$. Apparently we have the following relation $$\Delta T=T_2-T_1=-\int_{V_1}^{V_2}\frac{dV}{C_V}...
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1answer
57 views

Does no variables change in an adiabatic + isothermal system?

Adiabatic + isothermal = no heat and temperature change. Does that mean the system will remain as it is? If it is adiabatic + isovolumetric or adiabatic + isobaric , is it as well no change in any ...
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Is it possible to change one quantum state to another state by a cyclic adiabatic process?

An example is applying magnetic flux through the axis of a cylinder (2D system with periodic boundary condition). When changing flux from 0 to 1 flux quanta adiabatically, it seems that we can ...
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102 views

How do spin orientations change during adiabatic demagnetization of paramagnet?

Suppose a paramagnetic solid is taken on the following cycle, where $B_1 > B_2$ (1)->(2)->(3) I'm trying to explain what happens to occupation numbers in magnetic levels. Step (1) As $B_1$ ...
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What is the energy scale of a Hamiltonian?

On the second page of this paper a term 'fundamental energy scale' is used while talking about a Hamiltonian. The context is implementing Deutsch's algorithm using Adiabatic Quantum Computation. What ...
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Restriction on the value of adiabatic exponent

My instructor stated in his lecture that the maximum value of the adiabatic exponent, $\gamma$, can be 5/3 which is that of a monoatomic gas and that it cannot go below 1, but why is this so? He also ...
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Process both isothermal and adiabatic

Why a reversible process can't be both isothermal and adiabatic, while an irreversible one can be?
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Adiabatic Approximation, Solving the Schrödinger equation

In the adiabatic approximation one looks at the Hamiltonian $$ H_0 = \sum_{i = 1}^{N_e} \frac{\vec{p}_i^2}{2m_e} + \sum_{i < j} \frac{e^2}{|\vec{r}_i - \vec{r}_j|} + \sum_{k < l} \frac{Z_k ...
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Hannay's angle for a spin half interacting with a magnetic field that varies adiabatically over time

Does it make sense to talk about the Hannay's angle for a magnetic moment with spin 1/2?
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2answers
152 views

How to calculate work for irreversible adiabatic processes?

By the first law, we know $\text{d}U=\delta Q+\delta W$ and, on adiabats, we know $\text{d} U=\delta W$. But what is $\delta W$ for irreversible adiabatic processes? Take a thermally isolated ...
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Defining internal energy for adiabatically inaccessible states

As is well known, a good way to define the internal energy in classical thermodynamics is to define the difference in internal energy of two points as the amount of adiabatic work from one point to ...
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1answer
96 views

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 ...
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Internal energy of a reversible adiabatic process

what happens to the heat transfer and the internal energy in a system that undergoes reversible adiabatic process back to its original state. Bearing in mind that heat $Q$ was transferred at the ...
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1answer
236 views

Thermodynamics adiabatic transformation

I have the following question as howework, I think I don't have enough information to solve it. Given are $p_1=311$ kN/m$^2$, $T_1=333$ K, $T_2=853$ K. Asked are $p_2$, ratio $V_1/V_2$, and $R$ if ...