Density matrix Definition and 125 Threads

Thank you jensa.

I have a question about density matrices. Is there a way to deduce the purity of the density matrix just by inspection? -L

Hi, I have a particle physics exam tomorrow morning (in a few hours from now, in my time zone). I'm trying to figure out the whole reasoning behind pion-nucleon scattering. Please bear with me.. We write the scattering matrix as S = 1 - iT where T is given by T = f + i g...

Homework Statement to prove : square of density matrix= the density matrix itself (for a pure ensemble) Homework Equations density matrix=sum over P(i) ket(i) bra(i) where Pi = probability that random chosen system from ensemble shows state i. summed over i , where P=1 for pure ensemble The...

Why is the determinant of a mixed state density matrix always positive? In the specific case of a 2-dimensional Hilbert space, the density matrix (as well as any other hermitian matrix) can be expressed as \rho=\frac 1 2 (I+\vec r\cdot\vec \sigma) so its determinant is...

Could anyone help me to understand how the spin density matrix is invariant under unitary transformation?

Hi there, I am reading a text by Robert W. Boyd "Nonlinear optics", in page 228, he used pertubation theory on two-level system and let the steady-state solution of the dynamics equation of density matrix as w = w_0 + w_1 e^{-i\delta t} + w_{-1}e^{i\delta t} where w=\rho_{bb} - \rho_{aa}...

Hi there, I am thinking an interesting problem of spatial linewidth of two-level system. Suppose in some way I find out an element of the desinty matrix for the upper state of two-level system, \rho_{ee} and it turns out that \rho_{ee} is a function of a parameter G, which could be space...

In a density matrix, can some coherances (off diagonal terms) be zero while the diagonal terms(populations) aren't? I am confused because rhoij=Ci*Cj'. How can coherance be zero if Ci and Cj aren't?

For two level system , let denotes the ground state as 1 and exctied state as 2, for writing the office off-diagonal matrix element for the density operator, shall it be \rho_{12} = |2\rangle\langle 1| and \rho_{21} = |1\rangle\langle 2| ?

-- i know there were threads about reduced density matrix in this forum, but I am reading "Density-functional theory of atoms and molecules" by Parr R., Yang W., their notation is quite confusing to me... their notation is the same as shown in this page...

At the thermal equilibrium, the density matrix of a 2 spin-half system is given by: \begin{displaymath} \mathbf{\rho} = \left(\begin{array}{cccc} e^{-(1+c)/T} & 0 & 0 & 0\\ 0 & cosh[(1-c)/T] & -sinh[(1-c)/T] & 0\\ 0 & -sinh[(1-c)/T] & cosh[(1-c)/T] & 0\\ 0 & 0 & 0 & e^{-(1+c)/T}...

How to obtain the density matrix of the following system at thermal equilibrium? Given: Hamiltonian H :(in 4x4 matrix form) Hij = the i-th row and j-th column element of H H11 = (1+c)/2 H22 = -(1+c)/2 H23 = 1-c H32 = 1-c H33 = -(1+c)/2 H44 = (1+c)/2 where c is a parameter and all...

Hi, I am trying to calculate the time evolution of a density matrix. Like if there is a mixed state with 50% of |x, 0> and 50% of |y, 0>. After time t due to time evolution, the kets become: |x,t>= e^(-i/h Ht) |x,0> and so on. Is it ok to use these kets instead of the original ket to...

What is the arbitrary density matrix of a mixed state qubit?

Let we have two qubits A and B. First qubit has eigenstates |A0> and |A1>, and second has |B0> and |B1>. Let them be in the entangled state, described with vector c1 * |A0> * |B0> + c2 * |B0> * |B1>| where c1 and c2 are complex numbers with |c1|^2 + |c2|^2 = 1. Then what is density...

A superposition of states such as a_1|\psi_1\rangle+...+a_n|\psi_n\rangle represents a single physical state, a state for which the probability of a measurement finding the system in state |\psi_k\rangle is |a_k|^2. The a_k represent "quantum-type" probabilities. On the other hand the...

Homework Statement Suppose a source emits silver atoms, which are sent through three different types of Stern-Gerlach devices, each of them is either sorting the atoms along the x, y or z axis. If we preform a measurement along the z or y axis, the atoms are sorted in the ” + ”...

Let p1,p2 be two density matrices and M be a real, symmetric matrix. Now, <<p1|[M,p2]>>= <<p1|M*p2>>-<<p1|p2*M>>= Tr{p1*M*p2}-Tr{p1*p2*M}= 2i*Tr{(Im(p1|M*p2))}. Why is it that this works out as simply as (x+iy)-(x-iy)? How is Tr{p1*p2*m}=conjugate(Tr{p1*M*p2})? I can't seem to figure...

(1) How does one obtain the density matrix formalism for quantum fields from the path integral? (2) Suppose I have a box containing interacting particles of different kinds. Is it possible to incorporate into the density matrix formalism both a non-zero temperature T as well as a time t...

Let phi(x) and phi_dagger(x) be field operators which satisfy the appropriate commutation relations. Then is there any analytic approximation for the two particle density matrix given by <phi_dagger(x)phi_dagger(x')phi(x')phi(x)> Thanks!

We have a spin state described by a time-dependent density matrix \rho(t) = \frac{1}{2}\left(\mathbf{1}+\mathbf{r}(t)\cdot \mathbf{\sigma} \right) Initial condition for the motion is \mathbf{r} = \mathbf{r}_0 at t = 0. We are then asked to give a general expression for \rho(t) in terms of...

I'm starting to convince myself that the density matrix is a better way of describing a quantum state than a spinor, even in the case of pure states. But it seems like very few of my textbooks have much to say about density matrices. Any comments? Carl

While reading this article http://citebase.eprints.org/cgi-bin/fulltext?format=application/pdf&identifier=oai%3AarXiv.org%3Aquant-ph%2F9708045 (which is by the way very interesting) i've encountered two unknown terms: "reduced denstiy matrix" --- i have never heard this term before...

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...