Department of Physics and Astronomy

The Forbes Group

index

## Introduction

In our group we study the dynamical properties of quantum many-body systems ranging from cold atoms trapped in one of the coolest places in the universe -- to the neutron stars where matter is compressed to such extremes that a teaspoon would weight more than a mountain.

### Negative-Mass Hydrodynamics¶

Negative mass is a peculiar concept. Counter to everyday experience, an object with negative effective mass will accelerate backward when pushed forward. This effect is known to play a crucial role in many condensed matter contexts, where a particle's dispersion can have a rather complicated shape as a function of lattice geometry and doping. In our work we show that negative mass hydrodynamics can also be investigated in ultracold atoms in free space and that these systems offer powerful and unique controls.

### Michael McNeil Forbes¶

Our universe is an incredible place. Despite its incredible diversity and apparent complexity, an amazing amount of it can be described by relatively simple physical laws referred to as the Standard Model of particle physics. Much of this complexity "emerges" from the interaction of many simple components. Characterizing the behaviour of "many-body" systems forms a focus for much of my research, with applications ranging from some of the coldest places in the universe - cold atom experiments here on earth, to nuclear reactions, the cores of neutrons stars, and the origin of matter in our universe.

### Chunde Huang¶

Chunde comes from China where he got his MS in Computer Science from Xiamen University. Currently Chunde is working on non-linear optics and quantum monte carlo simulation.

### Ted Delikatny¶

Ted simulates various phenomena related to quantum turbulence in superfluids, including the dynamics and interactions of vortices, solitons, and domain wall dynamics. Currently Ted is working to understand the phenomenon of self-trapping in BECs with negative-mass hydrodynamics.

### Khalid Hossain¶

Khalid comes from Bangladesh where he got his MS in theoretical physics from University of Dhaka. Currently Khalid is simulating two-component superfluid mixtures - Spin-Orbit Coupled Bose Einstein Condensates (BECs) and mixture of Bose and Fermi superfluids. In particular, the interest is in detecting the entrainment (dragging of one component with another) effect, which may shed light on the astrophysical mystery of neutron star glitching.

### Md Kamrul Hoque Ome¶

Ome's primary fields of interest are theoretical nuclear and particle physics. In this regard, he is interested in using field theoretical and numerical techniques to solve equations that describe the subatomic phenomena.

Much of his recent investigations addresses the few-body nuclear physics via chiral effective field theory. In particular, he is studying the light nuclei (e.g. deuteron) at low energies where the effective degrees of freedom are pions and nucleons. Given the chiral potentials, the quantum mechanical analysis of the systems may improve our understanding of the properties of the nuclei.

He also enjoys strong coffee, reading books and being in intellectual environments.

### Ryan Corbin¶

In one of the oldest surviving writings in world language, an anonymous author (perhaps Solomon) wrote "For with much wisdom comes sorrow; the more knowledge, the more grief." As far as I can tell from the Timeline of the far future, this is still applicable today. We can have some fun on the way though!

Our universe is a fundamentally quantum one, and this is the universe I am fighting to understand. Currently I am trying to grasp existing techniques to probe many body systems in a computationally feasible way. Lately I have become interested in geometric physics, slow as I am to make progress. I am also working on my skills modeling core physics problems.

I have lived in Washington state most of my life; I hail from the greater Seattle area. Language is a big deal to me, and it should be to you as well. I read too much.

In [1]:
import mmf_setup;mmf_setup.nbinit()


This cell contains some definitions for equations and some CSS for styling the notebook. If things look a bit strange, please try the following:

• Choose "Trust Notebook" from the "File" menu.
• Re-execute this cell.

### Thermodynamics¶

This post discusses how phase equilibrium is established. In particular, we discuss multi-component saturating systems which spontaneously form droplets at zero temperature. This was specifically motivated by the discussion of the conditions for droplet formation in Bose-Fermi mixtures 1801.00346 and 1804.03278. Specifically, the following conditions in 1804.03278:

\begin{gather} \mathcal{E} < 0, \qquad \mathcal{P} = 0; \tag{i}\\ \mu_b\pdiff{P}{n_f} = \mu_f\pdiff{P}{n_b}; \tag{ii}\\ \pdiff{\mu_b}{n_b} > 0 , \qquad \pdiff{\mu_f}{n_f} > 0, \qquad \pdiff{\mu_b}{n_b}\pdiff{\mu_f}{n_f} > \left(\pdiff{\mu_b}{n_f}\right)^2. \tag{iii} \end{gather}

### Uncertainties¶

Here we discuss the python uncertainties package and demonstrate some of its features.

### Galilean Covariance¶

In his "Dialogue Concerning the Two Chief World Systems", Galileo put forth the notion that the laws of physics are the same in any constantly moving (inertial) reference frame. Consider a modern Lagrangian formulation of a classical object moving without a potential in 1D with coordinates $x$ and $\dot{x}$, and the same object in a moving frame with coordinates $X = x - vt$ and $\dot{X} = \dot{x} - v$. The Lagrangian and conjugate momenta in these frames are:

\begin{align} L[x, \dot{x}, t] &= \frac{m\dot{x}^2}{2}, & p &= \pdiff{L}{\dot{x}} = m\dot{x},\\ L_v[X, \dot{X}, t] &= \frac{m(\dot{X}+v)^2}{2}, & P &= \pdiff{L_v}{\dot{X}} = m(\dot{X}+v) = p. \end{align}

Perhaps surprisingly the conjugate momentum $P$ is the same in the moving frame whereas Galilean covariance indicates that in the moving frame one should have a description in terms of $P = m\dot{X} = p - mv$. In this post I clarify this difference, and elucidate the meaning of Galilean covariance in classical and quantum mechanics.

### Kamiak Cluster at WSU¶

Here we document our experience using the Kamiak HPC cluster at WSU.

#### Resources¶

##### General¶
• SLURM: Main documentation for the current job scheduler.
• Lmod: Environment module system.
• Conda: Package manager for python and other software.

### Prerequisites¶

This post describes the prerequisites that I will generally assume you have if you want to work with me. It also contains a list of references where you can learn these prerequisites. Please let me know if you find any additional resources particularly useful so I can add them for the benefit of others. This list is by definition incomplete - you should regard it as a minimum.

### Many-body Quantum Mechanics¶

In this notebook, we briefly discuss the formalism of many-body theory from the point of view of quantum mechanics.