Questions tagged [matrix-model]
A matrix model is a non-peturbative formulation of a theory, such as string theory based on Matrix quantum mechanics
46
questions
0
votes
1answer
19 views
Good starting point for quantum Hall matrix models
I am a recent Masters in theoretical condensed matter physics and have experience in working on topological insulators and Weyl semimetals. I have also dabbled a bit in the fractional quantum Hall ...
0
votes
0answers
28 views
Can we generalize matrix model theory?
As in the question, can matrix model theory be generalized to a tensor model theory? Will the results be different or useful in describing real world phenomena?
Details: in matrix model theory we ...
0
votes
0answers
14 views
How to incorporate refractive index in transfer matrix method
I need to determine the TE and TM reflections at the interface between a uniaxial crystal and air, using a matrix-based method, such as the TMM.
I can do so using the Fresnel equation with ease, but ...
0
votes
0answers
34 views
Correlation function of partition functions
In this paper the authors study the correlation function of partition functions defined by
$$\langle Z(\beta_1) \ldots Z(\beta_n) \rangle = \frac{1}{\mathcal{Z}}\int \mathrm{d}H \, \mathrm{e}^{-L \, \...
4
votes
1answer
55 views
$\delta^{(2)}$ convention
In this note: https://arxiv.org/abs/hep-th/0410165 at page 12 there is a delta-function constraint written as:
\begin{align}
\delta \left( ^ { U } M \right) = \prod _ { i < j } \delta ^ { ( 2 ) } \...
0
votes
0answers
47 views
Simultaneous shifted diagonalization of bunch of operators
I have the following Lie algebra which is generated by $\{L_n|n\geq 0\}.$ It satisfies the following commutation rule
$$ \Big[ L_i ,L_j \Big]= (i-j)(L_{i+j}-\frac14 L_{i+j-1}).....*$$
My question is ...
1
vote
0answers
29 views
Singular behavior of pure gravity
Can anyone plese explain what means singular part of partition function for pure gravity?
Let me specify my question. I am dealing with 2D quantum gravity and starts from path integral formulation of ...
1
vote
1answer
180 views
How to relate random matrix theory with Quantum mechanics approach
In Quantum mechanics we first built Hamiltonian and then find its eigenvalues and eigenvectors. How I can relate this with random matrix theory?
4
votes
0answers
85 views
How to calculate correlators in a 1D Conformally invariant Matrix Model?
I am working on a 1D Conformally invariant Matrix Model with the following Partition function:
$$
Z(g) = \int \mathcal{D}M(t) \exp \left[ -\text{tr}\int dt \left( \frac{1}{2} \dot{M}^2(t)+V(M) \...
3
votes
0answers
91 views
How to get the eigenvalue density contribution $\rho_1(x)$?
I'm studying the $1/N$ expansion beyond the planar limit in matrix models. Currently I'm trying to understand and reproduce the results of:
Antisymmetric Wilson loops in $\mathcal N \geq 4$ SYM ...
1
vote
2answers
273 views
Basis of eigenvectors common to H and B
Considering a three-dimensional state space spanned by the orthonormal basis formed by the three kets $|u_1\rangle,|u_2\rangle,|u_3\rangle $. In the basis of these three vectors, taken in order, are ...
2
votes
1answer
301 views
Hamiltonian matrix for a delta potential with periodic boundary condition
I'm trying to find the energy eigenvalues of a Dirac delta potential:
$$V(x)=-\alpha\delta(x)$$
with periodic boundary condition over some length $L$:
$$\psi(x+L)=\psi(x)$$
and only even ...
3
votes
0answers
106 views
Massless limit of Matrix Quantum Mechanics
I am working on a Matrix Quantum Mechanics model that is related to 2d string theory as defined here: http://arxiv.org/abs/hep-th/0311273 §Chapter III
The action is defined as $$
S = \text{Tr} \int ...
0
votes
0answers
23 views
Lumped mechanical system - Base Change and asymmetric matrices
Let's assume I have a system which can be wrote as:
$$ \underbrace{\begin{bmatrix}
m_{1} & 0 & \dots & 0 \\
0 & m_{2} & \...
3
votes
1answer
575 views
Gaussian beam propagation with ABCD matrix through a grin lens
I am currently trying to simulate a Gaussian beam that has a transverse offset of around 20um from the optic axis where the Gaussian beam travels through a grin lens using the ABCD matrix method. I ...
3
votes
1answer
129 views
Generalization of Itzykson-Zuber Formula to Path Integrals?
Some Background: In mathematical physics (matrix quantum mechanics in particular), one often runs into path integrals of the form:
$$ Z = \int \prod_{ab} DM^1_{ab}(\tau) DM^2_{ab}(\tau) e^{-NS(M^1,M^2,...
1
vote
1answer
291 views
References to Random Matrix Theory
I am looking for some good references - books/lecture notes/articles which contains Random Matrix Theory for Physicists. I am not particularly looking for mathematical rigor in derivations. I am more ...
1
vote
1answer
254 views
Relation between $1/N$ and perturbative expansions in QFT
I heard many times phrases like "large $N$ is a clever way to organize the diagrammatic expansion" or "each diagram in the large $N$ expansion contains an infinite number of usual perturbative ...
1
vote
0answers
61 views
Matching measured eigenvalue of a matrix [closed]
Given a Matrix of the form below, we have 8 variables, $\omega_{i}$ and $J_{ij}$. we want to diagonalise the Matrix to obtain values to match the observed Eigenvalue in an Experiment. i.e. $\bar{\...
9
votes
1answer
1k views
Examples of Matrix Product States
Matrix product states (MPS) are a way of representing a (many-body) wavefunction. The method has been described, for example, in
The density-matrix renormalization group in the age of matrix ...
10
votes
2answers
460 views
Emergence of space from quantum mechanics
Once talking to a visiting professor at my institute, I heard about some simple model that captures the emergence of space coordinates as the eigenvalues of some infinite-dimensional quantum ...
0
votes
2answers
444 views
How are unitary matrices and unitary random matrices associated with physics or quantum mechanics? [closed]
Please forgive my ignorance, my back ground is not physics. I am looking for distance measure between two unitary matrix (for my work). So my starting point is where else unitary matrix is applicable?...
1
vote
1answer
283 views
ADHM construction and Momentum Map
while I was reading about ADHM construction I had some troubles with precise geometrical identification of the various quantities. My doubts is well manifest in these two Wikipedia pages
1) ADHM ...
2
votes
0answers
174 views
Chern Simons Theory over S^3 as integral - what is domain of integration?
I found these nice lecture notes Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories so I am hoping to understand some parts of the Chern Simons theory better.
...
1
vote
0answers
128 views
Bloch's theorem for Semi-Infinite Lattice
If we have a lattice Hamiltonian $$ \sum_{n'\in\mathbb{Z}}H_{n,n'}\psi_{n'} = E\psi_{n} \,\forall n\in\mathbb{Z} $$
such that $ H_{n,n'} = H_{n+q,n'+q}$ for some $q\in\mathbb{N}$ and for all $\left(n,...
3
votes
1answer
587 views
On the Equivalence of Schrodinger and Heisenberg Descriptions of Quantum Mechanics and Observability
I'm not a physicist, but rather a control (feedback) systems engineer eager to understand more than just a cursory explanation of quantum mechanics. The StackExchange has been an excellent forum for ...
8
votes
1answer
4k views
What information does the trace of a matrix give?
I was recently thinking what information do we get from a matrix. So if we say the columns (or rows) of a matrix define the basis of a system, say vectors of 3 dimensional space. Then the determinant ...
1
vote
0answers
32 views
What is the current state of research about the Hayden-Preskill circuit? [duplicate]
Can someone summarize as to what are the problems and/or the open questions with the Hayden-Preskill circuit? (in the context of understanding black-holes or as a computer science question)It gives a ...
16
votes
1answer
526 views
Is there a physical interpretation to invariant random matrix ensembles?
Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ...
8
votes
1answer
199 views
The curvature of the space of commuting hermitian matrices
This is a question that I asked in the mathematics section, but I believe it may get more attention here. I am working on a project dedicated to the quantisation of commuting matrix models. In the ...
1
vote
1answer
1k views
What do matrices in the Gaussian orthogonal ensemble look like?
I've been reading a fair amount about quantum chaos, and random matrix theory comes up a lot. I get that they're looking at the distribution of eigenvalues from an ensemble of random matrices, but I ...
5
votes
0answers
256 views
Relation between holography and matrix models
Let's consider a 0-dimensional $N \times N$ Hermitean one matrix model.
It is defined by a potential V(M). Its partition function
is
$$Z = \int_{H_{N}} dM e^{-\frac{1}{g}V(M)}$$
where $H_{N}$ is the ...
1
vote
0answers
191 views
Matrix integral in multi-matrix model
Though it is a mathematical problem, maybe more physicists know it well.
In quiver matrix model which is reviewed DV or CKR, the path integral reduce to the matrix integral
$$Z \sim \int \prod_{i=1}^...
4
votes
0answers
120 views
Degrees of freedom in m(atrix) theory
The Hamiltonian for m(atrix) theory is given by
$$H=\frac{1}{2\lambda}\text{Tr}\left(P^{a}P_{a}+\frac{1}{2}\left[X^{a},X^{b}\right]^{2}+\theta^{T}\gamma_{a}\left[X^{a},\theta\right]\right).$$
Where $X^...
5
votes
1answer
308 views
Dimensional reduction of Yang-Mills to m(atrix) theory
The Yang-Mills action are usually given by $$S= \int\text{d}^{10}\sigma\,\text{Tr}\left(-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-\theta^{T}\gamma^{\mu}D_{\mu}\theta\right)$$
with the field strength defined ...
2
votes
1answer
642 views
Diagonalize mass matrix term for fermions and “doubling trick” in m(atrix) theory
Can someone help me understand the "Doubling trick" at page 36 in http://inspirehep.net/record/887513/files/sis-2002-060.pdf (named "Scattering in Supersymmetric M(atrix) Models" by Robert Helling) or ...
1
vote
0answers
155 views
Questions about Type HE Matrix String Theory
I was reading the heterotic string section of this thesis desertation by Luboš Motl, since I think I now understand the Type IIA Matrix String Theory. The only thing I knew about Type HE Matrix ...
asked Sep 28 '13 at 9:30
Abhimanyu Pallavi Sudhir
4,6464 gold badges27 silver badges45 bronze badges
7
votes
1answer
810 views
M(atrix) theory and things other than D0-branes? And is it non-peturbative M-theory or non-peturbative Type IIA theory?
When I first read the BFSS Paper on M(atrix)-theory, I was under the impression that it was a non-peturbative formulation of M-theory. But recently, upon reading this paper of Nathan Seiberg's, I ...
asked Jun 21 '13 at 9:48
Abhimanyu Pallavi Sudhir
4,6464 gold badges27 silver badges45 bronze badges
7
votes
0answers
265 views
$U(N)$ gauged quantum mechanics
I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic?
The action I am interested in is
$$...
4
votes
1answer
145 views
Schwarzschild radius in matrix models
The Schwarzschild radius for 11D BHs is given by $l_{11}(l_{11}m)^{1/8}$, which is the special case ($D=11$) of the general dimensional case of $(G_Dm)^{\frac{1}{D-3}}$. Here $m$ is the BH mass and $...
2
votes
1answer
201 views
M-theory on a Planck scale torus
We know that 11D M-theory is described by BFSS matrix model and for M-theory on a torus $T^p$ (at least for small $p$s) the description is given by SYM theory in $p+1$ dimensions by using the ...
2
votes
2answers
600 views
Path integral on matrix model
I was looking at a 0-dimensional matrix model, where the variables are $N\cdot N$ Hermitean matrices. It had a gauge symmetry, e.g. $U(N)$. And in the path integral, the Faddeev-Popov trick was used. ...
7
votes
1answer
212 views
random matrix ensembles from BMN model
My friends working on Thermalization of Black Holes explained solutions to their matrix-valued differential equations (from numerical implementation of the Berenstein-Maldacena-Nastase matrix model) ...
11
votes
2answers
2k views
Advanced topics in string theory
I'm looking for texts about topics in string theory that are "advanced" in the sense that they go beyond perturbative string theory. Specifically I'm interested in
String field theory (including ...
10
votes
1answer
125 views
Matrix geometry for F-strings
A stack of N D-branes has the strange property that the traverse D-brane coordinates are matrix-valued. When the matrices commute, they can be interpreted as ordinary coordinates for N ...
17
votes
1answer
3k views
Good introductory text for matrix string theory
Where can I find a good introductory text for matrix string theory? Most textbooks don't cover it, or only cover it very superficially.
What is the basic idea behind matrix string theory? How can ...
