In the last step to get result from a quantum computer, measurement is required to collapse the quantum state. This can be done by the measuring a large ensemble average of same computed result. One realization I know is to use NMR to measure billions of spin. So, what is the minimum number of...
Given a macro-state M of a system, let S denote the potion of the phase space that has the macro-state M.
A micro-canonical ensemble is one in which the probability of finding the micro-state in any part of S is equally likely (the density function is constant over S).
In Pathria's...
The ensemble interpretation of QM essentially ignores the wave function collapse, and apparently decoherence as well, by stating that only the statistical distributions within ensembles of systems matter (each system being in just one state).
My questions are:
Does the preparation of...
Consider an ensemble of one particle systems each evolving in one spatial dimension according to the non Hamiltonian equation of motion:
dx/dt=-ax
where x(t) is the position of the particle at time t and a is a constant. The compressibility of this system...
Homework Statement
1.a. analyze an ideal gas in a two dimensional world using micro-canonical ensemble. Specifically, find the equation of state (surface tension and area will replace pressure and volume) and also the energy as a function of temperature. b. modify the equation to create a “van...
Hi all,
I was brushing up on statistical ensembles, and I found something apparently weird in
microcanonical treatment of the ideal "classical" gas. I'm mainly following K. Huang's
Statistical Mechanics.
So there's a first approach to the problem in which the MC entropy is evaluated
via an...
Hi all,
this is about problem 8.2 in Huang's Statistical Mechanics.
I think I've been able to solve it, but the solution raised a question about
the Maxwell-Boltzmann distribution. So first I provide my solution to the
problem, then discuss the apparently weird point.
Homework...
Homework Statement
The entropy in the microcanonical ensemble is defined in terms of omega(E), the number of states such that total energy be E. compute (as a function of total energy E,total number of particles N and magnetic field h) N+ the number of particles i with sigma= +1 and N- where...
Homework Statement
An ice sheet forms on a lake. The air above the lake is at \Delta T (<0), while the water below the ice sheet is at 0°C. Assume that the heat of fusion of the water freezing on the lower surface is conducted through the sheet to the air above. How much time does it take to...
Homework Statement
In the canonical ensemble, the probability that a system is in state r is given by
P_i = \frac{g_i \exp (-\beta E_i)}{\sum_i g_i \exp( -\beta E_i)}
where g_i is the multiplicity of state i. This is confusing me because I thought
P_i = \frac{g_i}{\sum_i g_i} = states...
Homework Statement
Grand Canonical ensemble problem- A surface of N sites that can have 0,1,2 atoms. It costs no energy to adsorb an atom. Grand canonical problem therefore in contact with particle reservoir. Assume \mu chem potentiol and temp T.
What is probability for site to be empty,1,or 2...
Hello!
I have a question arising from my course in statistical physics: Describing microcanonical, canonical and grandcanonical ensemble you take three variables (like E,V,N for microncanonical) and get the "rest" from derivatives of the free energies. Is there a deeper meaning why there are...
Four spin1 particles are rigidly fixed at four corners of a square.
1. What will be the entropy.
2. A field is now applied that produces an energy difference between m=0 and m=1,-1 states of each of each particle. Take m=0 as the ground state and find the free energy at temperature T.
3. Find...
I've been studying and thinking about statistical physics for a couple days now... and what bothers me is the grand canonical partition function. Namely that for a system with fixed chemical potential and energy \epsilon_i the probability of having N_i particle in that state is proportional to...
Homework Statement
In a microcanonical ensemble is entropy constant? Since there is only one macrostate of energy.
The Attempt at a Solution
I think so.
im a bit confused about which interpretation is experimentally favored,wave function collapse or the 'minimalist ensemble interpretation (ala L.E Ballentine' (as Doc Al wrote somewhere)?All the older literature talks about 'reduction of wave packet' but reading Ballentine has left me confused.
Hey folks, I really need help setting up a canonical ensemble.
I am using the einstein model and have an energy:
E_\nu=A + \sum_{i=1}^{2N} \hbar\omega n_i+\sum_{j=1}^{N} \hbarh\omega n_j
where A is some constant.
Now, I need to build the partition function which I 'think' looks like...
Hi there,
I have a system with the following energy using the einstein model:
E_\nu=\sum_{i=1}^{2N} h\omega n_i+\sum_{j=1}^{N} h\omega n_j
I need to set up a canonical ensemble for this.
How would I write the partition function please?
Hi,
I'm taking a course in Stat Mach using Kerson and Huang's Statistical Mechanics book. I am quite confused with their treatment of a Gibbsian Ensemble. They say imagine an infinite copies of the same system whose state can be represented by a point in phase space. Then \rho (p,q,t) =...
I am trying to make the connection from statistical mechanics to thermodynamics for the isothermal isobaric ensemble. Partition function = (sum of)exp(-BEj-gamma*Vj).
I have followed T.L. Hill [Statistical Mechanics, p. 67] but can not understand how he justifies dE=(sum of)EdP, rather than...
Can someone explain to me about the van Leeuwen problem in classical stat physics and give me a complete step by step solutions to the problem.
I am a graduate student doing MS. I am new to statistical mechanics. So please explian as one should explain it to an ms student.
i have basic...
Hi I am just doing an undergraduate degree in physics and currently studying a course in the foundations of QM.
The problem I want to solve is this:
There is an ensemble in a state corresponding to vector (i, 2)
A measurement of Sy (with the operator represented by the 2x2 pauli spin...
Hi, can someone please explain the exact notion of an ensemble to me please?
In the canonical ensemble, how do ensembles exchange energy between one another?
what is the significance of keeping the temperature fixed?
thanks
I am taking a statictical mechanics course, and one thing bothers me. I am not sure when we should use the normal partition function (Z) and when the grand partition function (twisty Z). In particular, why can we not use grand partition function when we are considering the following system...