Debamalya Dutta

National Institute of Science Education and Research | NISER · School of Physical Sciences

Similarity transformation to make a Hamiltonian diagonal look like U^{\dagger}HU. What about an observable and density matrix? How do they transform?

Link: https://physics.stackexchange.com/q/781022/147579

Attaching mathematical expressions here is problematic. I am attaching the link to the question here.

link: https://physics.stackexchange.com/q/782250/147579

If someone can help me understand Helicity in the context of the High Harmonic Generation, it will be helpful. Due to mathematical notations, the exact question can be found "https://physics.stackexchange.com/questions/778274/what-is-helicity-in-high-harmonic-generation".

I want to install arpack-ng(https://github.com/opencollab/arpack-ng). I am using open PBS Linux cluster without sudo permission. All of my libraries are installed in non-default directory, like g++, gfortran, openmpi, eigen, anaconda, python almost everything is in non-default directory. In this case how to install arpack-ng?

I have tried to install Using autotools(uses ./configure), but it always failed in every possible way I have tried in the cluster. The problem mainly arises at time when I run ./configure command. Whereas when I have tried in my local machine where most of the things are installed in default directory, then I was able to install arpack-ng in non-default directory

I know that δ(f(x))=∑δ(x−xi)/f′(xi). What will be the expression if "f" is a function of two variables, i.e. δ(f(x,y))=?

As it is not possible to show mathematical expressions here I am attaching link to the question.

link: https://math.stackexchange.com/q/4700487/1136237

Your expertise in determining and comprehending the boundaries of integration within the Delta function's tantalizing grip will be treasured beyond measure.

I am seeking to solve a first-order complex matrix differential equation of the form dy/dt=c.H.y, where H is a complex matrix with complex elements, and c is a complex number. Python and cpp offer built-in libraries like 'odeint', 'solve ivp', and 'boost odeint' that can tackle this problem with ease. However, I am facing a challenge finding a suitable package in Fortran that can handle complex numbers and solve this type of ODE effectively. I have explored options such as 'odepack', but it can't handle complex numbers.

Your assistance will be much appreciated.

Kindly look at my question in the following link.

link: https://stackoverflow.com/questions/75804325/why-mpicxx-is-uble-to-compile-cpp-code-includes-boost-library

As it is impossible to use equations here, I am posting the link to my question here.

Link: https://math.stackexchange.com/q/4650679/1136237

I am using Boost ODEINT C++ to solve a simple differential equation with two different steppers: "runge_kutta_cash_karp54" and "runge_kutta_fehlberg78". According to the Boost website, "runge_kutta_cash_karp54" has a 5th-order error estimation and "runge_kutta_fehlberg78" has an 8th-order error estimation, which means "runge_kutta_fehlberg78" should be more accurate. However, when I solve a differential equation like "dy/dx=pxsin(x)", "runge_kutta_cash_karp54" produces more accurate results than "runge_kutta_fehlberg78" which I have compared with Mathematica result. On the other hand, for a differential equation like "dy/dx=1/(p-x)" with a singularity at "x=p", "runge_kutta_cash_karp54" throws an error in the limit of [-5,5] for p=1, which is expected, but "runge_kutta_fehlberg78" does not throw an error. I am very confused about this behaviour and would appreciate any suggestions for the detailed documentation of each individual stepper.

I am attaching the code.

Like solve_ivp or odeint in python, which shows warning messages if there arises any discrepancy during runtime, in Boost odint we need to create observer for that. I just want to know is there any predefined observer exist to handel all kind of errors and warnings message, or we have to creat for our own?

I have checked in boost odeint there are odeint_error.hpp and exception.hpp, but they can't be used directly.

The answer to the question will not be straightforward as the conventional Hamiltonian in the EM field. As it is difficult to write equations here, I am attaching the link to the question.

Question link: https://physics.stackexchange.com/q/749166/147579

I am absolutely new in c++ programming and facing many problems converting a simple python code in c++.

Mainly I am facing four following problems in writing python code in c++.

I generally prefer to use the libraries like 'Eigen', 'odeint' etc for reliability. But using libraries in c++ is much harder than in python. I want to convert the code from python to c++ for speed. The following code is written in parallel processing using 'pool'. For each 'Time' it takes a huge amount of time in python.

In the python code I have used 'odeintw' for solving complex differential systems of equations instead of 'solve_ivp' for better speed and 'nquad' instead of 'dblquad' for double integration to increase the 'limit: 500' from default 'limit: 50'.

It will be very much helpful if someone helps me to write the python code in c++.

For example, if I have a matrix differential equation; dy/dt=A(t).y. Here my jacobian is the A(t) matrix. But what is derivative across the column or derivative across the row as it is mentioned in 'col_deriv'?

I have tried both col_deriv=0 and col_deriv=1, but the result does not change.

For example, consider a differential equation as in the image(.jpg file). What are the available functional forms of f(t), for which one could exactly write the analytical form of y(t)?

In crystals that obey inversion symmetry retain their polarization form in x-->-x, we can prove that even order susceptibilities get canceled. But I want to know if there exists any way that I can explicitly show that even order transition amplitudes are not contributing to the Higher-order Harmonic Generation in this particular crystals.