“Within Ourselves”: The Development of British Light Infantry in North America during the Seven Years’ War

The first British regulars to appear in North America were those accompanying a small British expedition to wrest Manhattan from the Dutch in 1664. Colonel Richard Nicolls’ troops landed on Long Island 25 August 1664 at the exact site where General William Howe’s troops would disembark over a century later. After a swift Dutch capitulation, Nicolls’ redcoats and subsequent garrisons of British regulars would maintain a solid presence in New York for a virtually uninterrupted period of 119 years. It has been suggested by one American historian that this factual record has been conveniently overlooked by most of his colleagues in order that “the dismal episode of Braddock’s defeat” can figure prominently in history books as the first appearance of British redcoats on the North American scene. Thus “they could be made to appear as stupid brutes led by an eighteenth century Colonel Blimp while American militia simultaneously appeared as a keen and valiant yeomanry led by that paragon of all virtue and destined military hero of the fight for American liberty, George Washington.” His accusation is a valid one, but not very surprising, as much of early American history has become firmly embedded in myth, legend and folklore. “Braddock’s Defeat,” “The Massacre at Fort William Henry,” “The Boston Massacre” and even “George Washington’s Cutting Down the Cherry Tree” have all served a variety of purposes down through the centuries. All have become part of the “usable past” and have been extensively deployed in any discussions of one of those favourite themes of North American historians—the conflict between European and colonial values and methods. Inevitably European warfare vs. North American warfare (la petite guerre) has been drawn into the mythic vortex. Canadian historian I.K. Steele writes that “North American pride in the ways of the New World has often led to the assumption that, in warfare as in everything else, the new men of the New World were better than the history-laden men of the Old.” Braddock’s defeat more than any other engagement of the Seven Years’ War has, “with some misrepresentation,” been used as key evidence to support this assumption of superiority. Stanley Pargellis reinforces this view: Military historians hold that Braddock’s defeat taught a lesson badly needed for the time: you cannot employ parade ground tactics in the bush. To almost everyone who in one connection or another remembers Braddock, this episode stands as a conflict between Old World and New World ways, with the outcome justifying the new. However, many historians led by Pargellis, with Paul Koppermans, Ian Strachan, and Steele in close support, stress that Braddock’s defeat can no longer be perceived or used as such. While broad generalizations about the utility of close-order formations in woods or the cunning and ruthlessness of Indian tactics or the command abilities of the young Washington may all be still true, they are not true as inferences from Braddock’s defeat. The general consensus now is that Braddock’s debacle was precipitated in large part by his critical neglect on the day of battle to observe the fundamental rules of war laid down in the European manuals of the day. His leadership lapse and complacency once nearing his objective meant that his soldiers were never given a chance to demonstrate that Old World methods, properly applied, might have very well won the day. His column from the day it launched into the North American wilderness adopted well-conceived and generally well-executed security measures as per the manuals. On the day however, these careful measures were inexplicably not ordered nor implemented by Braddock and his staff and their absence was enough to ensure the ruin of their army and give British officers a reputation for ineptitude under frontier conditions. This reputation is undeserved, for British regulars took especial care to prepare themselves for the American theatre, including Braddock and subsequent commanders. After Braddock’s defeat no inferior guerilla force would ever overcome any substantial body of British regulars during the Seven Years’ War in North America

Comment on "Phase separation in a two-species Bose mixture"

In an article in 2007, Mishra, Pai, and Das [Phys. Rev. A 76, 013604 (2007)] investigated the two-component Bose-Hubbard model using the numerical DMRG procedure. In the regime of inter-species repulsion $U^{ab}$ larger than the intra-species repulsion $U$, they found a transition from a uniform miscible phase to phase-separation occurring at a finite value of $U$ , e.g., at around $U = 1.3$ for $\Delta = U^{ab}/U = 1.05$ and $\rho_{a} = \rho_{b} = 1/2$. In this comment, we show that this result is not correct and in fact the two-component Bose-Hubbard model is unstable to phase-separation for any $U^{ab} > U > 0$.Comment: 2 pages, 3 figures, submitted to Phys. Rev.

Published work on freshwater science from the FBA, IFE and CEH, 1929-2006

A new listing of published scientific contributions from the Freshwater Biological Association (FBA) and its later Research Council associates – the Institute of Freshwater Ecology (1989–2000) and the Centre for Ecology and Hydrology (2000+) is provided. The period 1929–2006 is covered. The compilation extends an earlier list assembled by in 1979

Chebyshev matrix product state approach for time evolution

We present and test a new algorithm for time-evolving quantum many-body systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011)]. The approach is based on merging the matrix product state (MPS) formalism with the method of expanding the time-evolution operator in Chebyshev polynomials. We calculate time-dependent observables of a system of hardcore bosons quenched under the Bose-Hubbard Hamiltonian on a one-dimensional lattice. We compare the new algorithm to more standard methods using the MPS architecture. We find that the Chebyshev method gives numerically exact results for small times. However, the reachable times are smaller than the ones obtained with the other state-of-the-art methods. We further extend the new method using a spectral-decomposition-based projective scheme that utilizes an effective bandwidth significantly smaller than the full bandwidth, leading to longer evolution times than the non-projective method and more efficient information storage, data compression, and less computational effort.Comment: 14 pages, 8 figure

Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment

We propose an environment recycling scheme to speed up a class of tensor network algorithms that produce an approximation to the ground state of a local Hamiltonian by simulating an evolution in imaginary time. Specifically, we consider the time-evolving block decimation (TEBD) algorithm applied to infinite systems in 1D and 2D, where the ground state is encoded, respectively, in a matrix product state (MPS) and in a projected entangled-pair state (PEPS). An important ingredient of the TEBD algorithm (and a main computational bottleneck, especially with PEPS in 2D) is the computation of the so-called environment, which is used to determine how to optimally truncate the bond indices of the tensor network so that their dimension is kept constant. In current algorithms, the environment is computed at each step of the imaginary time evolution, to account for the changes that the time evolution introduces in the many-body state represented by the tensor network. Our key insight is that close to convergence, most of the changes in the environment are due to a change in the choice of gauge in the bond indices of the tensor network, and not in the many-body state. Indeed, a consistent choice of gauge in the bond indices confirms that the environment is essentially the same over many time steps and can thus be re-used, leading to very substantial computational savings. We demonstrate the resulting approach in 1D and 2D by computing the ground state of the quantum Ising model in a transverse magnetic field.Comment: 17 pages, 28 figure

Valence bond entanglement entropy of frustrated spin chains

We extend the definition of the recently introduced valence bond entanglement entropy to arbitrary SU(2) wave functions of S=1/2 spin systems. Thanks to a reformulation of this entanglement measure in terms of a projection, we are able to compute it with various numerical techniques for frustrated spin models. We provide extensive numerical data for the one-dimensional J1-J2 spin chain where we are able to locate the quantum phase transition by using the scaling of this entropy with the block size. We also systematically compare with the scaling of the von Neumann entanglement entropy. We finally underline that the valence-bond entropy definition does depend on the choice of bipartition so that, for frustrated models, a "good" bipartition should be chosen, for instance according to the Marshall sign.Comment: 10 pages, 6 figures; v2: published versio

Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems

The driven-dissipative Bose-Hubbard model can be experimentally realized with either negative or positive onsite detunings, inter-site hopping energies, and onsite interaction energies. Here we use one-dimensional matrix product density operators to perform a fully quantum investigation of the dependence of the non-equilibrium steady states of this model on the signs of these parameters. Due to a symmetry in the Lindblad master equation, we find that simultaneously changing the sign of the interaction energies, hopping energies, and chemical potentials leaves the local boson number distribution and inter-site number correlations invariant, and the steady-state complex conjugated. This shows that all driven-dissipative phenomena of interacting bosons described by the Lindblad master equation, such as "fermionization" and "superbunching", can equivalently occur with attractive or repulsive interactions.Comment: single column 12 pages, 4 figures, 1 tabl

The Miscible-Immiscible Quantum Phase Transition in Coupled Two-Component Bose-Einstein Condensates in 1D Optical Lattices

Using numerical techniques, we study the miscible-immiscible quantum phase transition in a linearly coupled binary Bose-Hubbard model Hamiltonian that can describe low-energy properties of a two-component Bose-Einstein condensate in optical lattices. With the quantum many-body ground state obtained from density matrix renormalization group algorithm, we calculate the characteristic physical quantities of the phase transition controlled by the linear coupling between two components. Furthermore we calculate the Binder cumulant to determine the critical point and draw the phase diagram. The strong-coupling expansion shows that in the Mott insulator regime the model Hamiltonian can be mapped to a spin 1/2 XXZ model with a transverse magnetic field.Comment: 10 pages, 10 figures, submitted to Phys. Rev.