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Theories of Quantum Gravity predict a minimum measurable length and a corresponding modification of the Heisenberg Uncertainty Principle to the so-called Generalized Uncertainty Principle (GUP). However, this modification is non-relativistic, making it unclear whether the minimum length is Lorentz invariant. We formulate a Relativistic Generalized Uncertainty Principle, resulting in a Lorentz invariant minimum measurable length and the resolution of the composition law problem. This proved to be an important step in the formulation of Quantum Field Theory with minimum length. We derived the Lagrangians consistent with the existence of minimal length and describing the behaviour of scalar, spinor, and $U(1)$ gauge fields. We calculated the Feynman rules (propagators and vertices) associated with these Lagrangians. Furthermore, we calculated the Quantum Gravity corrected scattering cross-sections for a lepton-lepton scattering. Finally, we compared our results with current experiments, which allowed us to improve the bounds on scale at which quantum gravity phenomena will become relevant.

CAP Virtual Congress 2021

Quantum field theory with minimum length

effective field theory

relativistic generalized uncertainty principle

quantum gravity phenomenology

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technical paper

Effective local therapy is needed to avoid local progression of the tumor, which may further decrease the development of systemic metastases and increase the possibility for resection. Radiation therapy (RT) is frequently used to locally treat the tumor. One of the major issues in RT for treating cancer is the close proximity of adjacent organs at risk, resulting in treatments doses being limited by significant tissue toxicities, preventing dose escalation necessary to guarantee local control. One of the currently adapted approaches to overcome this challenge is to add radiosensitizers to current RT protocol to unlock the full potential of RT. In this talk, I will focus on gold nanoparticles (GNPs), docetaxel, and cisplatin as radiosensitizers. About half of cancer patients (50%) receive radiotherapy, and all of these patients would benefit from this type of novel approaches.

Combining gold nanoparticles with other radiosensitizers for unlocking the full potential of cancer radiotherapy

Blister formation occurs when a laser pulse is focussed through a transparent substrate onto a coated polymer thin film. A pocket of expanding vapor is formed beneath the film, which pushes the film upward locally. This process has been used for Laser-Induced Forward Transfer (LIFT) of materials. Most studies of blister formation and blister-based LIFT use linear absorption of nanosecond or picosecond lasers to obtain large target areas (~100s of µm$^2$). We are the first to achieve nanoscale blisters, through nonlinear absorption of femtosecond pulses.

We spin-coated polyimide films achieving a thickness of 1.3 µm. We used a Ti:Sapphire laser producing pulses of 45-fs duration at a central wavelength of 800 nm. We mounted samples onto a 3D motion stage, and focused single pulses of various energies through the glass substrate onto the polymer-glass interface. Since polyimide is transparent to 800 nm light, we used tightly-focused (NA ≥ 0.4) femtosecond pulses to induce nonlinear absorption. We characterized samples after blister fabrication using atomic force microscopy (AFM). At intensities above 10$^{13}$ W/cm$^2$, interactions of the pulse with both the film and substrate must be considered. We model these interactions and find that the resulting blister volume is proportional to the energy deposited in the film.

The use of 0.95 NA focusing led to a minimum structure diameter of 700 nm, smaller than the wavelength of the laser pulse. In the future, we propose the use of thinner films and shorter wavelengths to reach further into the nanoscale. This technique can be used for direct micro- and nano-fabrication, and potentially to LIFT sensitive materials on the nanoscale. It is a possible alternative to lithography, laser milling, and laser-based additive machining that also leaves the surface composition unchanged, since the laser energy is deposited beneath the film.

Nanoscale polymer blister formation using single femtosecond pulses

The prototypical superfluid, Helium-4 ($^4$He), transitions to its superfluid state below ~2 K. In contrast, its isotopic counterpart Helium-3 ($^3$He) has a transition temperature of ~2 mK. This thousand-fold disparity is due to the nature of the superfluid transition; while $^4$He Bose condenses directly, the fermionic $^3$He atoms must first form composite bosons through Cooper pairing. The $p$-wave, spin-triplet pairing of the $^3$He atoms gives rise to many possible superfluid phases, though only two distinct phases are realized in the bulk.

Recent experimental and theoretical advances have suggested that a third phase emerges when superfluid $^3$He is confined to a slab --- a pair-density-wave (PDW) phase. Analogous to a supersolid, the PDW phase is characterized by the spontaneous breaking of translational symmetry that coexists with superfluid order. The precise spatial structure of this "superfluid crystal" has been the subject of ongoing debate: existing theories favor a unidirectional PDW, the stripe phase, while recent nuclear magnetic resonance (NMR) experiments seem to indicate a two-dimensional PDW with square or hexagonal symmetry. In this talk, I will outline a mechanism, based on Landau's theory of weak crystallization, which stabilizes a two-dimensional PDW with the hexagonal symmetry of a triangular lattice.

Triangular Pair-Density-Wave in Confined Superfluid 3He

The main advantage of hybrid PET-MR imaging systems is the ability to correlate anatomical with metabolic information directly. The bulk of commercially available PET-MR systems are quite large and expensive and mostly used on humans rather than for preclinical animal studies. This has led to a gap of knowledge in PET-MR imaging of small animal models used in preclinical research. Our work takes advantage of a new imaging system developed by Cubresa called 'NuPET'. This device is a MR-compatible PET scanner placed around the subject while they are within the toroidal bore of a MR scanner. With this equipment we are attempting to demonstrate the selective activation of serotonergic neurons in living rodent brains. To specify which neurons are to be activated, we use Designed Receptors Exclusively Activated by Designer Drug (DREADD) technology. These DREADDs are designer G-protein-coupled receptors. Neurons at the site of a stereotactic injection are transfected with a viral vector containing the proteins necessary to force expression of DREADDs in genetically modified rats. These may then be activated by administering the designer drug clozapine-N-oxide (CNO). This technique allows for precise spatiotemporal control of receptor signaling in vivo. Over two experiments (N=5, N=2) we have attempted to image the effect of DREADDs-mediated excitation of 5-HT neurons in rats. Voxel-based analysis of the data thus far show no confirmed statistically significant differences between rats given saline and those given CNO. Numerous methodological issues have been discovered within the experimental design, and are being addressed for a new trial of the technique and technology.

The authors wish to acknowledge funding from NSERC partnership grants, Mitacs, Cubresa, and Research Manitoba.

Multi-modal PET-MR imaging of the selective activation of serotonergic neurons in living rodent brains with DREADD technology

Multiquark states have been of great interest among hadronic physicists, and despite the big breakthrough that came in 2003 with the discovery of the charmonium-like tetraquark candidate X(3872), their internal quark structure (e.g., molecular versus diquark clusters) are not well-understood yet. QCD sum-rule mass estimates for multiquark states can provide insights on possible internal quark structures. Previous research suggests that the next-to-leading order (NLO) corrections to QCD sum-rule mass determinations are quite different in heavy and light multiquark states. 
The study of these multiquark systems can give us another approach to understand strong interactions at the elementary level and at different energy scales. The goal of this research is a detailed examination of the NLO corrections to mass estimates of the light scalar tetraquarks using QCD sum-rules.

NLO effects on light tetraquark mass estimates using QCD sum rules

We present some analytic results that describe the gluon field, or glasma, that exists at very early times after a collision of relativistic heavy ions at proper time $\tau=0$. We use a Colour Glass Condensate approach, and perform an expansion in $\tau$. We show that the expansion to order $\tau^6$ can be trusted to about $\tau=0.05$ fm/c. We calculate the transverse and longitudinal pressures and show that for $\tau < 0.05$ fm/c they move towards their equilibrium values of one third of the energy density. We study the spatial eccentricity of the plasma, and the Fourier coefficients of the azimuthal momentum distribution. Our results for the Fourier coefficients are larger than  expected, which contradicts the usual assumption that anisotropy is mostly generated during the hydrodynamic evolution of the plasma. We  find a significant correlation between the elliptic flow coefficient and the eccentricity, which indicates that the spatial inhomogeneity introduced by the initial geometry is effectively transmitted to the azimuthal distribution of the gluon momentum field, even at very early times. This result is interesting because correlations of this kind are  characteristic of the onset of hydrodynamic behaviour. We also calculate the angular momentum of the glasma and obtain results that are many orders of magnitude smaller than the initial angular momentum of two ions colliding with non-zero impact parameter. This indicates that most of the angular momentum carried by the valence quarks is not transmitted to the glasma. The result is significant because it contradicts the picture of a rapidly rotating initial glasma state,  but agrees with the current lack of experimental evidence for a global polarization effect in the hyperons and vector mesons produced in heavy ion collisions.

Characteristics of early time gluon fields in relativistic heavy ion collisions

I will discuss different notions of nonrelativistic strings and their target space geometries. The first example comes from a self-contained corner of string theory dubbed nonrelativistic string theory, which is closely related to string theory in the discrete light-cone quantization. The appropriate spacetime geometry for nonrelativistic string theory is a stringy generalization of Newton-Cartan geometry. The second example involves sigma models at a Lifshitz point, which describe strings moving in bimetric spacetime. In the limit when the two metrics coincide, the relativistic sigma model that underlies string theory can be recovered. This study of Lifshitz-type sigma models also provides useful insights for constructing a quantum theory of membranes.

Nonrelativistic Strings and Exotic Geometries

Despite the constant stream of black hole merger observations, black hole mergers are not yet fully understood. The phenomenon seems simple enough, but the details of how the two apparent horizons end up as one horizon is unclear due to the non-linear nature of the merger process. Recent numerical work has shown that there is a merger of self-intersecting Marginally Outer-Trapped Surfaces (MOTS) during the black hole merger. Following papers have investigated further into MOTS in a simpler and static scenario, that of a Schwarzschild black hole. Such cases require less machinery and are solved with everyday computers. Those numerical calculations show an infinite number of self-intersecting MOTS hidden within the apparent horizon, as well as open surfaces (MOTOS). The importance of Schwarzschild MOTS are not to be undermined due to its relative simplicity as such MOTS describe an extreme-mass-ratio black hole merger, where one of the black holes is far more massive than the other. In this talk, I will discuss the current understanding of black hole mergers as have numerically been shown and my work investigating Schwarzschild MOTS in maximally-extended Kruskal-Szekeres coordinates.

The many marginally outer trapped surfaces of Schwarzschild spacetime

Topological insulators are an interesting class of materials which host distinct zero/low-energy states at their boundaries. These symmetry-protected states can, for example, arise as Majorana zero-modes in various superconducting systems and have potential applications in quantum error correction. However, experimental study and verification of such zero-modes remains a challenge. Considering a toy-system based on the Su-Schrieffer-Heeger (SSH) model coupled to one end with a semi-infinite conducting lead, we propose a measurement method for gapped topological states through a study of the decoherence dynamics of a quantum dot or qubit. Decoherence rates along the length of the SSH chain vary proportionally to the edge states and allow for both the identification and spatial characterisation of such states.

Quantum dots as probes for topological materials

We use Langevin dynamics (LD) simulations to investigate single file diffusion (SFD) in a dilute solution of flexible linear polymers inside a narrow tube. The transition from single-file diffusion, where the mean-square displacement scales like $\langle x^2 \rangle \sim t^{1/2}$, to normal diffusion with $\langle x^2 \rangle \sim t$, is studied as a function of the system parameters, such as the width of the channel, the polymer concentration and the polymer size. Based on our simulation results and scaling arguments, we propose a phase diagram describing the different diffusion regimes. We also map this problem onto a one-dimensional Lattice Random Walk algorithm where the diffusing object represents the polymer's center of mass. In order to model the polymers entanglement and disentanglement processes we allow several objects to temporarily share the same lattice site and diffuse together. Extension of our work to polydisperse polymer solutions, one-dimensional electrophoresis, ring polymers and DNA mapping are discussed.

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Quantum field theory with minimum length

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