Dec 272014
 

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I recently picked up two books on Lie groups and algebras.  The first I read was Lie Groups for Pedestrians, by Harry Lipkin.  As the title suggests, this book is an introduction to Lie groups.  The author tries to hide most of the mathematical complexity of Lie’s theory and focuses on examples from physics.  The book is easy to read, but it seems to me that it is really designed for the typical pedestrian that circulates near the elementary particle physics section of physics department.  I found it somewhat useful and at time interesting.

Robert Gilmore’s Lie Groups, Lie Algebras, and Some of Their Applications is a nice introduction to Lie’s theory written from the perspective of a mathematician.  I really liked Gilmore’s introductory chapters that so neatly summarize various topics propaedeutic to the study of Lie groups and algebras (field, group, vector space, algebra).  Applications to quantum mechanics are scattered throughout the book and tend to focus on simple aspects (spin, the SU(2) group, second quantization).  Lie’s theory is pretty involved and so even this book, at times, can be challenging to read.

Why am I interested in Lie algebras and groups?  Lie algebras are at the basis of second quantization techniques.  Some results from Lie algebra are used in many-body theory, for example the Baker–Campbell–Hausdorff formula.  However, the aspect that is most interesting for me is the connection between the formalism of generalized normal ordering of Mukherjee and Kutzelnigg and Lie and Hopf algebras.

 December 27, 2014  Book review Comments Off on Books on Lie algebras and groups
Dec 202014
 
  • Tensor product methods and entanglement optimization for ab initio quantum chemistry. This review of tensor product approximations in quantum chemistry by Szalay et al. was just posted on arXiv. At times a bit formal, this is a nice introduction to the topic.
  • In Search of a Rational Dressing of Intermediate Effective Hamiltonians. This is a paper on intermediate Hamiltonian theory, an approach to deal with the intruder state problem in effective Hamiltonian theories. From the abstract: The intermediate effective Hamiltonians are designed to provide M exact energies and the components of the corresponding eigenvectors in the N-dimensional model space, with N > M. The effective Hamiltonian is not entirely defined by these N × M conditions, and several dressings of the Hamiltonian matrix in the model space are possible.
  • Appointing silver and bronze standards for noncovalent interactions: A comparison of spin-component-scaled (SCS), explicitly correlated (F12), and specialized wavefunction approaches. A systematic investigation of the accuracy of non-covalent interaction predicted with various quantum chemical methods by Burns and co-workers. From the abstract: After examination of both accuracy and performance for 394 model chemistries, SCS(MI)-MP2/cc-pVQZ can be recommended for general use, having good accuracy at low cost and no ill-effects such as imbalance between hydrogen-bonding and dispersion-dominated systems or non-parallelity across dissociation curves. Moreover, when benchmarking accuracy is desirable but gold-standard computations are unaffordable, this work recommends silver-standard [DW-CCSD(T**)-F12/aug-cc-pVDZ] and bronze-standard [MP2C-F12/aug-cc-pVDZ] model chemistries, which support accuracies of 0.05 and 0.16 kcal/mol and efficiencies of 97.3 and 5.5 h for adenine·thymine, respectively.
 December 20, 2014  Uncategorized No Responses »
Oct 262014
 

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I recently purchased a couple dozen books for the group and out of curiosity decided to add this book to the order. Although I don’t use integrals much in my research (we mostly deal with linear algebra and tensor algebra) I found this book to be extremely interesting. It’s so interesting that I cannot stop reading it and put it down.
Inside Interesting Integrals is a great book if you want to revisit your integration skills and learn all sorts of tricks to compute definite integrals.

 October 26, 2014  Uncategorized No Responses »
Oct 112014
 

Construction in our new space has finished and so yesterday we had a party to celebrate!

New Room Party Oct-2014

 October 11, 2014  Group news Comments Off on Inauguration party
Oct 042014
 

In the past two weeks I read two papers from arXiv that present some very interesting new ideas.  The first paper, Extended Møller-Plesset perturbation theory for dynamical and static correlations, by Takashi Tsuchimochi and Troy Van Voorhis, deals with symmetry restoration in second-order perturbation theory.  The extended MP2 method presented by the authors looks promising and I found it very interesting because it can automatically adapt to single- and multireference problems.  At the very end of the paper the authors even show that their technique can be used to compute excited states.

The second one,Compact wavefunctions from compressed imaginary time evolution, is from Jarrod R. McClean and Alán Aspuru-Guzik.  This paper mixes compression techniques with a propagation of the Schrödinger equation in imaginary time to compute the ground state energy.

 

 October 4, 2014  Uncategorized No Responses »
Aug 072014
 

Renovations of the Emerson Center have finally begun! Soon the Emerson Center will have four more cubicles for visitors and a nice lunch/discussion room that will permit students and researchers to exchange ideas over a meal or a coffee.

IMG_2201

 

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 August 7, 2014  Group news No Responses »
Apr 222014
 

Lanczos
Once in a while you stumble in a good book, and for me recently that was Applied Analysis by Cornelius Lanczos, published by Dover Books. This is a little gem of numerical analysis, and although it is a bit outdated, it is a book full of interesting tidbits of knowledge.

 April 22, 2014  Tips No Responses »
Apr 212014
 

I recently decided that I ought to have a canonical set of colors to use in my publications and so I came up with the following seven colors:

Color palette

Here are gnuplot definitions of lines using these colors. Feel free to use this set, and if you have suggestion on how to improve it, let me know!

# Canonical colors - full line
set style line 1 lc rgb '#000000' lt 1 lw 3.0 ps 0.5 pt 7 # black
set style line 2 lc rgb '#16469D' lt 1 lw 3.0 ps 0.5 pt 7 # dark blue
set style line 3 lc rgb '#BD202D' lt 1 lw 3.0 ps 0.5 pt 7 # red
set style line 4 lc rgb '#00A14B' lt 1 lw 3.0 ps 0.5 pt 7 # green
set style line 5 lc rgb '#4B96D1' lt 1 lw 3.0 ps 0.5 pt 7 # light blue
set style line 6 lc rgb '#F16521' lt 1 lw 3.0 ps 0.5 pt 7 # orange
set style line 7 lc rgb '#9F6EAF' lt 1 lw 3.0 ps 0.5 pt 7 # light purple
# Canonical colors - dashed line
set style line 11 lc rgb '#000000' lt 2 lw 3.0 ps 0.5 pt 7 # black
set style line 12 lc rgb '#16469D' lt 2 lw 3.0 ps 0.5 pt 7 # dark blue
set style line 13 lc rgb '#BD202D' lt 2 lw 3.0 ps 0.5 pt 7 # red
set style line 14 lc rgb '#00A14B' lt 2 lw 3.0 ps 0.5 pt 7 # green
set style line 15 lc rgb '#4B96D1' lt 2 lw 3.0 ps 0.5 pt 7 # light blue
set style line 16 lc rgb '#F16521' lt 2 lw 3.0 ps 0.5 pt 7 # orange
set style line 17 lc rgb '#9F6EAF' lt 2 lw 3.0 ps 0.5 pt 7 # light purple

 April 21, 2014  Research, Tips No Responses »